1
What is the LCM of 15, 20 and 25?
Correct answer: A. 300
Prime factors: 15 = 3 × 5, 20 = 2² × 5, 25 = 5². LCM = 2² × 3 × 5² = 300.
easy
LCM, HCF and Number System MCQs
Solved mathematics MCQs on LCM and HCF, remainders, divisibility, primes, factors, unit digits and recurring decimals, for PPSC, FPSC and NTS tests.
20 MCQsUpdated 30 October 2026
This set covers LCM and HCF word problems (bells, remainders and smallest or largest numbers), divisibility rules, prime numbers, the number of factors, unit digits of powers, remainders and recurring decimals.
Prime factorisation solves most LCM and HCF questions in seconds. Every answer here was calculated and checked by script, and each explanation shows the shortest method.
- 2
What is the HCF of 84 and 126?
Correct answer: B. 42
84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. The common factors give 2 × 3 × 7 = 42.
easy - 3
What is the HCF of 36, 60 and 84?
Correct answer: C. 12
36 = 2² × 3², 60 = 2² × 3 × 5 and 84 = 2² × 3 × 7. The common part is 2² × 3 = 12.
easy - 4
What is the LCM of 8, 12 and 18?
Correct answer: D. 72
8 = 2³, 12 = 2² × 3 and 18 = 2 × 3². LCM = 2³ × 3² = 72.
easy - 5
The product of two numbers is 1,350 and their HCF is 15. What is their LCM?
Correct answer: A. 90
For two numbers, product = HCF × LCM, so LCM = 1,350 ÷ 15 = 90.
medium - 6
The HCF and LCM of two numbers are 6 and 180. If one number is 36, what is the other?
Correct answer: B. 30
Other number = (HCF × LCM) ÷ first number = (6 × 180) ÷ 36 = 30. Check: HCF(36, 30) = 6 and LCM(36, 30) = 180.
medium - 7
What is the smallest number which, when divided by 12, 15 and 20, leaves a remainder of 5 each time?
Correct answer: C. 65
The LCM of 12, 15 and 20 is 60; add the remainder: 60 + 5 = 65.
medium - 8
What is the largest number that divides 62 and 98, leaving a remainder of 2 in each case?
Correct answer: D. 12
Subtract the remainder first: 60 and 96. Their HCF, 12, is the required number.
hard - 9
Three bells ring at intervals of 6, 8 and 12 minutes. If they ring together at 9:00 a.m., after how many minutes will they next ring together?
Correct answer: A. 24 minutes
They ring together again after the LCM of 6, 8 and 12, which is 24 minutes (at 9:24 a.m.).
medium - 10
What is the smallest four-digit number exactly divisible by 15, 20 and 30?
Correct answer: B. 1,020
The LCM of 15, 20 and 30 is 60. The first multiple of 60 above 999 is 1,020 (60 × 17).
hard - 11
Which one of 91, 119, 127 and 133 is a prime number?
Correct answer: C. 127
91 = 7 × 13, 119 = 7 × 17 and 133 = 7 × 19, but 127 has no factor up to √127 (about 11.3), so it is prime.
medium - 12
How many prime numbers are there between 1 and 50?
Correct answer: C. 15
They are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47: 15 primes.
medium - 13
What is the sum of the first 20 natural numbers?
Correct answer: D. 210
Sum = n(n + 1) ÷ 2 = 20 × 21 ÷ 2 = 210.
easy - 14
Which of these numbers is divisible by 9?
Correct answer: B. 4,563
A number is divisible by 9 when the sum of its digits is. 4 + 5 + 6 + 3 = 18; the other digit sums are 16, 17 and 17.
easy - 15
What is the unit (last) digit of 7²³?
Correct answer: B. 3
The units digits of powers of 7 repeat every 4: 7, 9, 3, 1. 23 ÷ 4 leaves remainder 3, so the units digit is the third in the cycle: 3.
Read detailshard - 16
What is the remainder when 2¹⁰ is divided by 7?
Correct answer: A. 2
2¹⁰ = 1,024 = 7 × 146 + 2, so the remainder is 2.
medium - 17
How many factors (divisors) does 36 have?
Correct answer: B. 9
36 = 2² × 3², so the number of factors is (2 + 1)(2 + 1) = 9: 1, 2, 3, 4, 6, 9, 12, 18 and 36.
medium - 18
What is the smallest number that must be added to 1,000 to make it exactly divisible by 7?
Correct answer: B. 1
1,000 ÷ 7 leaves a remainder of 6, so adding 1 gives 1,001 = 7 × 143.
medium - 19
What is the largest three-digit number exactly divisible by 13?
Correct answer: D. 988
999 ÷ 13 = 76 remainder 11, so 999 − 11 = 988 (13 × 76).
medium - 20
The recurring decimal 0.222… is equal to which fraction?
Correct answer: B. 2/9
Let x = 0.222…; then 10x = 2.222…, so 9x = 2 and x = 2/9.
medium