All Free Mathematics MCQs with Answers

• A. 30/7
• B. 30/98
• C. 60/147
• D. 50/294

Explanation: For the standard least-common-multiple interpretation of fractions, 30/7 works because (30/7) ÷ (6/7) = 5, (30/7) ÷ (5/14) = 12, and…

• A. 196
• B. 630
• C. 1260
• D. 2520Election Officer Mcqs

Explanation: First find LCM(12, 18, 21, 30) = 1260. If the number is n, then 2n must equal the least such common multiple, so 2n = 1260 and n = 630.

• A. 7/8
• B. 13/16
• C. 31/40
• D. 63/80

Explanation: Convert the fractions to a common denominator of 80: 7/8 = 70/80, 13/16 = 65/80, 31/40 = 62/80, and 63/80 remains 63/80.

• A. 276
• B. 299
• C. 322
• D. 345

Explanation: If the HCF is 23 and the other factors of the LCM are 13 and 14, the two numbers are 23 x 13 = 299 and 23 x 14 = 322.

• A. 24
• B. 48
• C. 56
• D. 60

Explanation: The HCF must always divide the LCM, because every common divisor is a factor of every common multiple.

• A. 1
• B. 117
• C. equal to their H.C.F
• D. Cannot be calculated

Explanation: For coprime numbers, the HCF is 1, so their LCM equals their product. Hence the LCM is 117, since the product is 117.

• A. 55/601
• B. 601/55
• C. 11/120
• D. 120/11

Explanation: The product of two numbers equals their HCF x LCM = 5 x 120 = 600. Therefore the sum of their reciprocals is (sum of numbers) ÷ (product)…

• A. 279
• B. 283
• C. 308
• D. 318

Explanation: Using product = HCF x LCM, the product of the two numbers is 11 x 7700 = 84700.

• A. 40
• B. 80
• C. 120
• D. 200

Explanation: Write the numbers as 3x, 4x and 5x. Since 3, 4 and 5 are pairwise coprime, their LCM is 3 x 4 x 5 x = 60x; hence 60x = 2400, so x = 40.

• A. 28
• B. 32
• C. 40
• D. 64Islamic Studies Quiz

Explanation: Let the numbers be 2x and 3x. Their LCM is 6x, so 6x = 48 gives x = 8; the sum is 2 x 8 + 3 x 8 = 40.

• A. 75
• B. 81
• C. 85
• D. 89

Explanation: Since 551 = 19 x 29 and 1073 = 29 x 37, the common middle number is 29.

• A. 1
• B. 2
• C. 3
• D. 4

Explanation: If the H.C.F. is 13, write the numbers as 13a and 13b, where a and b are co-prime. Then 13a x 13b = 2028, so ab = 2028/169 = 12.

• A. 101
• B. 107
• C. 111
• D. 185

Explanation: Write the numbers as 37a and 37b because their H.C.F. is 37. Then ab = 4107/(37 x 37) = 3, so the co-prime factors are 1 and 3, giving…

• A. 4
• B. 6
• C. 8
• D. 12

Explanation: Let the numbers be 33a and 33b. Then a + b = 528/33 = 16, and a and b must be co-prime because the H.C.F. is exactly 33.

• A. 12
• B. 16
• C. 24
• D. 48

Explanation: The numbers are 3k and 4k, and because 3 and 4 are co-prime, their H.C.F. is k.

• A. 4, 8, 12
• B. 5, 10, 15
• C. 10, 20, 30
• D. 12, 24, 36

Explanation: The ratio 1:2:3 has H.C.F. 1, so multiplying every term by 12 gives numbers 12, 24 and 36. Their H.C.F. is 12, as required.

• A. 22 * 35 * 72
• B. 22 * 53 * 72
• C. 25 * 52 * 72
• D. 23 * 35 * 72

Explanation: Using the superscript notation, the required L.C.M. is 2^4 x 3^5 x 5^2 x 7^2.

• A. 0.03
• B. 0.9
• C. 0.18
• D. 0.108

Explanation: Remove the decimals by multiplying all numbers by 100: 108, 36 and 90. Their H.C.F. is 18, so the decimal H.C.F. is 18/100 = 0.18.

• A. 120
• B. 240
• C. 360
• D. 480

Explanation: Prime factors are 24 = 2^3 x 3, 36 = 2^2 x 3^2 and 40 = 2^3 x 5. The L.C.M.

• A. 4
• B. 6
• C. 12
• D. 18Education

Explanation: The factors common to 36 and 84 include 1, 2, 3, 4, 6 and 12, with 12 being the greatest.