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Number System, HCF–LCM and Simplification MCQs

HCF and LCM, unit digits, divisibility, remainders, factors, BODMAS simplification, square and cube roots, with step-by-step solutions.

20 MCQsUpdated 27 October 2026

This set covers HCF and LCM, unit digits of powers, sums of natural numbers, square and cube roots, divisibility rules and the simplification of expressions.

Unit digits of powers repeat in a cycle of at most four, so divide the power by 4 and use the remainder. Shortcuts like this save valuable time.

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  1. 1

    What is the HCF of 48 and 72?

    Correct answer: A. 24

    48 = 2⁴ × 3 and 72 = 2³ × 3², so the HCF = 2³ × 3 = 24.

    easy
  2. 2

    What is the LCM of 15, 20 and 25?

    Correct answer: B. 300

    15 = 3 × 5, 20 = 2² × 5, 25 = 5². LCM = 2² × 3 × 5² = 300.

    easy
  3. 3

    What is the smallest number which, when divided by 6, 8 and 12, leaves a remainder of 5 in each case?

    Correct answer: B. 29

    LCM of 6, 8 and 12 = 24. Add the remainder: 24 + 5 = 29.

    medium
  4. 4

    The HCF of two numbers is 12 and their product is 1728. What is their LCM?

    Correct answer: D. 144

    For two numbers, HCF × LCM = product, so LCM = 1728 ÷ 12 = 144.

    medium
  5. 5

    What is the unit digit of 7^85?

    Correct answer: A. 7

    Unit digits of powers of 7 repeat every 4: 7, 9, 3, 1. 85 ÷ 4 leaves remainder 1, so the unit digit is 7.

    medium
  6. 6

    What is the unit digit of 2^50?

    Correct answer: A. 4

    Powers of 2 end in 2, 4, 8, 6 in turn. 50 ÷ 4 leaves remainder 2, so the unit digit is 4.

    medium
  7. 7

    Simplify: 18 + 12 ÷ 4 × 3 − 5

    Correct answer: D. 22

    Division and multiplication first, left to right: 12 ÷ 4 = 3, 3 × 3 = 9. Then 18 + 9 − 5 = 22.

    easy
  8. 8

    Simplify: (25 − 5) × 2 + 36 ÷ 6

    Correct answer: D. 46

    Brackets: 20. Then 20 × 2 = 40 and 36 ÷ 6 = 6. Total = 46.

    easy
  9. 9

    What is the sum of the first 50 natural numbers?

    Correct answer: D. 1,275

    Sum = n(n + 1) ÷ 2 = 50 × 51 ÷ 2 = 1,275.

    easy
  10. 10

    What is the sum of the first 20 odd numbers?

    Correct answer: C. 400

    The sum of the first n odd numbers is n², so 20² = 400.

    medium
  12. 11

    What is the average of all whole numbers from 11 to 30?

    Correct answer: B. 20.5

    For consecutive numbers the average is (first + last) ÷ 2 = (11 + 30) ÷ 2 = 20.5.

    easy
  13. 12

    What is the square root of 1,764?

    Correct answer: A. 42

    42 × 42 = 1,764, so √1764 = 42.

    easy
  14. 13

    What is the cube root of 2,197?

    Correct answer: C. 13

    13 × 13 × 13 = 2,197.

    medium
  15. 14

    Simplify: 3/8 + 5/12

    Correct answer: C. 19/24

    LCM of 8 and 12 is 24: 9/24 + 10/24 = 19/24 (≈ 0.79).

    medium
  16. 15

    Which decimal is equal to 1/8?

    Correct answer: C. 0.125

    Divide 1 by 8: 1 ÷ 8 = 0.125 (one-eighth is half of one-quarter, 0.25).

    easy
  17. 16

    Which of these numbers is prime?

    Correct answer: A. 97

    97 has no divisor other than 1 and itself. 91 = 7 × 13, 87 = 3 × 29 and 93 = 3 × 31.

    medium
  18. 17

    Find the digit x if the number 52x4 is divisible by 9.

    Correct answer: B. 7

    A number is divisible by 9 when its digit sum is. 5 + 2 + x + 4 = 11 + x must be 18, so x = 7 (5,274 = 9 × 586).

    medium
  19. 18

    Which of these numbers is divisible by 8?

    Correct answer: A. 2,464

    A number is divisible by 8 when its last three digits are. 464 ÷ 8 = 58, so 2,464 is divisible by 8.

    medium
  20. 19

    What is the remainder when 1,000 is divided by 7?

    Correct answer: C. 6

    7 × 142 = 994, and 1,000 − 994 = 6.

    easy
  21. 20

    How many factors (divisors) does 360 have?

    Correct answer: B. 24

    360 = 2³ × 3² × 5. Number of factors = (3 + 1)(2 + 1)(1 + 1) = 24.

    hard