This page gives you 60 HCF & LCM questions to sharpen your number skills. The set starts simple and slowly gets tricky. You are going to get problems on divisibility, common factors, and common multiples. Some questions are direct, and some are word problems. Check the answers and solutions to learn faster methods.
More aptitude topics are organized here: aptitude question and answers.
List of 30 HCF and LCM Formulas
1. Highest Common Factor (HCF)
Definition: The greatest number that divides two or more numbers exactly.
2. Least Common Multiple (LCM)
Definition: The smallest number that is exactly divisible by two or more numbers.
3. Product Formula for Two Numbers
Formula:
HCF × LCM = Product of the two numbers
That is: HCF(a, b) × LCM(a, b) = a × b
4. Formula to Find One Number
Formula:
Second Number = (HCF × LCM) ÷ First Number
5. Numbers in the Form of HCF
Formula:
If the HCF of two numbers is H, then the numbers can be written as:
H × x and H × y
where x and y are coprime numbers.
6. HCF and LCM by Prime Factorization
HCF: Product of common prime factors with the smallest powers
LCM: Product of all prime factors with the greatest powers
7. Greatest Number Dividing Given Numbers Exactly
Formula:
Required number = HCF of the given numbers
8. Smallest Number Divisible by Given Numbers
Formula:
Required number = LCM of the given numbers
9. Greatest Number Dividing Given Numbers Leaving the Same Remainder
Formula:
Required number = HCF of the differences of the numbers
That is, for numbers a, b, c:
Required number = HCF(b – a, c – b, c – a)
10. Least Number Leaving the Same Remainder When Divided by Several Numbers
Formula:
Required number = LCM of the divisors + common remainder
11. Least Number to Be Added or Subtracted for Exact Divisibility
Number to be added = LCM – remainder when the given number is divided by the LCM
Number to be subtracted = remainder when the given number is divided by the LCM
12. Greatest Possible Measure, Length, Tile Size or Group Size
Formula:
Required measure = HCF of the given quantities
13. Least Time After Which Events Coincide Again
Formula:
Required time = LCM of the time intervals
14. Greatest and Least n-Digit Number Divisible by Given Numbers
Greatest n-digit number:
Required number = Largest n-digit number – remainder when it is divided by the LCM
Least n-digit number:
Required number = Smallest n-digit number + [LCM – remainder]
if the remainder is not zero.
15. Co-prime Numbers
Formula:
If two numbers are co-prime, then:
HCF = 1
LCM = Product of the numbers
60 HCF & LCM Problems: Aptitude Questions (With Answers)
HCF & LCM Aptitude Test: Core Skills (20 MCQs)
Question 1. Find the HCF of 84, 126 and 210.
a) 21
b) 42
c) 84
d) 14
Answer:
b) 42
Question 2. Find the LCM of 18, 24 and 40.
a) 480
b) 240
c) 360
d) 120
Answer:
c) 360
Question 3. The HCF and LCM of two numbers are 12 and 252 respectively. If one number is 84, find the other number.
a) 36
b) 24
c) 28
d) 42
Answer:
a) 36
Question 4. Find the HCF of 96 and 144.
a) 48
b) 72
c) 24
d) 36
Answer:
a) 48
Question 5. Find the LCM of 75 and 120.
a) 300
b) 600
c) 150
d) 1200
Answer:
b) 600
Question 6. Find the HCF of 105, 140 and 175.
a) 5
b) 7
c) 70
d) 35
Answer:
d) 35
Question 7. What is the greatest number that divides 251, 407 and 563 leaving the same remainder in each case?
a) 52
b) 78
c) 156
d) 12
Answer:
c) 156
Question 8. The HCF and LCM of two numbers are 21 and 420 respectively. If one number is 84, find the other number.
a) 105
b) 60
c) 140
d) 96
Answer:
a) 105
Question 9. If HCF(45, 60) = 15, find LCM(45, 60).
a) 150
b) 240
c) 120
d) 180
Answer:
d) 180
Question 10. A number when divides 392, 560 and 728 leaves remainder 8 each time. Find the greatest such number.
a) 12
b) 48
c) 24
d) 16
Answer:
c) 24
Question 11. Find the LCM of 12, 15, 20 and 27.
a) 540
b) 1080
c) 270
d) 360
Answer:
a) 540
Question 12. Find the HCF of (2^4 × 3^2 × 5) and (2^3 × 3^3 × 5^2).
a) 1080
b) 720
c) 180
d) 360
Answer:
d) 360
Question 13. Find the HCF of 176 and 264.
a) 44
b) 88
c) 22
d) 132
Answer:
b) 88
Question 14. Find the LCM of 96 and 132.
a) 1056
b) 528
c) 1320
d) 792
Answer:
a) 1056
Question 15. Find the LCM of 48, 60 and 90.
a) 1440
b) 240
c) 360
d) 720
Answer:
d) 720
Question 16. Find the LCM of 8, 9 and 21.
a) 336
b) 630
c) 252
d) 504
Answer:
d) 504
Question 17. What is the greatest 4-digit number divisible by both 12 and 18?
a) 9972
b) 9990
c) 9960
d) 9984
Answer:
a) 9972
Question 18. Two numbers are 45 and 63. Find the least positive number x such that LCM(45, 63, x) = 2520 and HCF(45, 63, x) = 9.
a) 72
b) 8
c) 36
d) 144
Answer:
a) 72
Question 19. Find the greatest number that divides 1001, 2002 and 3003 exactly.
a) 91
b) 143
c) 7
d) 1001
Answer:
d) 1001
Question 20. Find the HCF of 240 and 360.
a) 80
b) 180
c) 60
d) 120
Answer:
d) 120
HCF & LCM Aptitude Test: Remainders and Least Number Conditions (20 Challenging MCQs)
Question 1. Find the least positive number that is divisible by 6, 8 and 15 and leaves remainder 2 when divided by each.
a) 124
b) 120
c) 242
d) 122
Answer:
d) 122
Question 2. Find the least positive number that leaves remainder 1 when divided by 5, 7 and 9.
a) 317
b) 316
c) 315
d) 631
Answer:
b) 316
Question 3. Find the least positive number that leaves remainder 3 when divided by 8, 12 and 20.
a) 120
b) 123
c) 243
d) 121
Answer:
b) 123
Question 4. Find the least positive number that leaves remainder 11 when divided by 12, 15 and 18.
a) 180
b) 191
c) 371
d) 181
Answer:
b) 191
Question 5. Find the least positive number N such that N leaves remainders 1, 2 and 3 when divided by 2, 3 and 4 respectively.
a) 35
b) 23
c) 7
d) 11
Answer:
d) 11
Question 6. Find the least positive number that leaves remainder 5 when divided by 9, 10 and 12.
a) 185
b) 365
c) 181
d) 180
Answer:
a) 185
Question 7. Find the least positive number that leaves remainders 10, 11 and 12 when divided by 11, 12 and 13 respectively.
a) 1716
b) 1715
c) 1727
d) 1703
Answer:
b) 1715
Question 8. Find the least positive number that leaves remainder 1 when divided by 4, 6 and 9.
a) 36
b) 73
c) 19
d) 37
Answer:
d) 37
Question 9. Find the least positive number N such that N leaves remainders 1, 2 and 3 when divided by 5, 6 and 7 respectively.
a) 416
b) 206
c) 196
d) 41
Answer:
b) 206
Question 10. Find the least positive number that leaves remainders 7, 8 and 9 when divided by 8, 9 and 10 respectively.
a) 359
b) 719
c) 349
d) 360
Answer:
a) 359
Question 11. Find the least positive number that is divisible by 7, 9 and 12 and leaves remainder 2 when divided by 5.
a) 312
b) 252
c) 126
d) 502
Answer:
b) 252
Question 12. Find the least positive number that leaves remainder 6 when divided by 7 and remainder 10 when divided by 11.
a) 81
b) 153
c) 76
d) 230
Answer:
c) 76
Question 13. Find the least positive number that leaves remainder 7 when divided by 16 and remainder 3 when divided by 12.
a) 55
b) 23
c) 39
d) 87
Answer:
c) 39
Question 14. Find the least positive number that when divided by 13 leaves remainder 5 and when divided by 9 leaves remainder 5.
a) 239
b) 122
c) 5
d) 125
Answer:
b) 122
Question 15. Find the least positive number that is divisible by 18 and 30 and leaves remainder 7 when divided by 11.
a) 900
b) 810
c) 540
d) 1260
Answer:
b) 810
Question 16. Find the least positive number N such that N is divisible by 12 and leaves remainder 9 when divided by 10.
a) 9
b) 69
c) 129
d) No solution
Answer:
d) No solution
Question 17. Find the least positive number that leaves remainder 4 when divided by 6, remainder 5 when divided by 7, and remainder 6 when divided by 8.
a) 334
b) 166
c) 502
d) 166
Answer:
b) 166
Question 18. Find the least positive number that is divisible by 24 and leaves remainder 5 when divided by 7.
a) 72
b) 96
c) 120
d) 120
Answer:
b) 96
Question 19. Find the least positive number that leaves remainder 2 when divided by 9 and remainder 3 when divided by 8.
a) 83
b) 11
c) 59
d) 59
Answer:
a) 83
Question 20. Find the least positive number that leaves remainder 3 when divided by 5 and remainder 4 when divided by 6.
a) 9
b) 27
c) 39
d) No correct option
Answer:
d) No correct option
HCF & LCM Aptitude Test: Multi-Constraint Word Problems (20 Challenging MCQs)
Question 1. Two numbers are in the ratio 3:5 and their HCF is 14. Find their LCM.
a) 140
b) 70
c) 210
d) 420
Answer:
c) 210
Question 2. Two numbers are in the ratio 4:7 and their LCM is 840. Find their HCF.
a) 30
b) 15
c) 20
d) 60
Answer:
a) 30
Question 3. The HCF of two numbers is 18 and their product is 11664. Find their LCM.
a) 972
b) 1296
c) 324
d) 648
Answer:
d) 648
Question 4. The LCM of two numbers is 2310 and their HCF is 15. If one number is 210, find the other number.
a) 105
b) 165
c) 150
d) 180
Answer:
b) 165
Question 5. What is the least number that must be added to 1470 so that the result is divisible by both 24 and 35?
a) 30
b) 70
c) 420
d) 210
Answer:
d) 210
Question 6. Three bells ring at intervals of 18 s, 24 s and 30 s. If they ring together now, after how many minutes will they ring together again?
a) 9
b) 3
c) 6
d) 12
Answer:
c) 6
Question 7. To tile a rectangular floor of size 84 m × 126 m using the largest possible square tiles, what should be the side of each square tile?
a) 21
b) 42
c) 28
d) 63
Answer:
b) 42
Question 8. Find the least positive number that is divisible by 12, 15 and 18 and leaves remainder 2 when divided by 7.
a) 360
b) 900
c) 1080
d) 1260
Answer:
c) 1080
Question 9. The LCM of two numbers is 1680 and their HCF is 40. If one number is 240, find the other number.
a) 320
b) 280
c) 420
d) 200
Answer:
b) 280
Question 10. Two numbers have HCF 6 and LCM 420. If their difference is 54, find the larger number.
a) 96
b) 70
c) 84
d) 90
Answer:
c) 84
Question 11. What is the least number that must be added to 96 so that the result is divisible by both 15 and 18?
a) 90
b) 84
c) 24
d) 54
Answer:
b) 84
Question 12. Find the least positive number that leaves remainder 1 when divided by 9, 12 and 15, and is also divisible by 7.
a) 901
b) 361
c) 721
d) 541
Answer:
c) 721
Question 13. What is the greatest 3-digit number that is divisible by 6, 8 and 12?
a) 972
b) 960
c) 996
d) 984
Answer:
d) 984
Question 14. A ribbon of length 252 m is to be cut into equal pieces of maximum length such that the pieces can also exactly measure 198 m and 144 m ribbons. What is the maximum length of each piece?
a) 18
b) 24
c) 36
d) 28
Answer:
a) 18
Question 15. The LCM of 30, 72 and x is 360 and the HCF of 30, 72 and x is 6. What is the greatest value of x less than 100?
a) 72
b) 96
c) 90
d) 60
Answer:
c) 90
Question 16. Find the least positive number that is divisible by 16, 18 and 20 and leaves remainder 5 when divided by 7.
a) 2160
b) 720
c) 1440
d) 2880
Answer:
c) 1440
Question 17. The HCF of 24, 36 and x is 12 and their LCM is 360. Find the least value of x.
a) 120
b) 60
c) 30
d) 180
Answer:
b) 60
Question 18. A traffic signal flashes every 48 s, another every 60 s, and a third every 75 s. If they flash together at 10:00:00, at what time will they flash together next?
a) 10:30:00
b) 10:15:00
c) 10:20:00
d) 10:25:00
Answer:
c) 10:20:00
Question 19. A contractor wants to arrange 168, 210 and 294 bricks into identical stacks with the maximum number of bricks per stack (no leftovers). How many bricks will be in each stack?
a) 84
b) 21
c) 14
d) 42
Answer:
d) 42
Question 20. The HCF and LCM of two numbers are 13 and 2470 respectively. If one number is 130, find the other number.
a) 190
b) 494
c) 260
d) 247
Answer:
d) 247
FAQs on HCF and LCM
1. What is the difference between HCF and LCM?
HCF is the greatest number that divides two or more numbers exactly. LCM is the smallest number that is exactly divisible by two or more numbers.
2. When should I use HCF in a question?
Use HCF when the question asks for the greatest, largest, highest, or maximum possible size, length, or equal grouping.
3. When should I use LCM in a question?
Use LCM when the question asks for the least, smallest, first common, next common, or minimum number that is divisible by the given numbers.
4. Why do time-based problems usually use LCM?
Problems about bells, traffic lights, or repeated events use LCM because we need to find the next time all of them will happen together again.
