Which of these numbers is a multiple of 24?

Correct option is C

A number is a multiple of 24 if it is divisible by both 8 and 3.

Step 1: Check divisibility by 8.

A number is divisible by 8 if the last three digits of the number are divisible by 8.

63810: Last three digits are 810. 810 ÷ 8 = 101.25 (not divisible)

31256: Last three digits are 256. 256 ÷ 8 = 32 (divisible)

53784: Last three digits are 784. 784 ÷ 8 = 98 (divisible)

35718: Last three digits are 718. 718 ÷ 8 = 89.75 (not divisible)

Step 2: Check divisibility by 3.

A number is divisible by 3 if the sum of its digits is divisible by 3.

63810: Sum of digits = 6 + 3 + 8 + 1 + 0 = 18. 18 ÷ 3 = 6 (divisible)

31256: Sum of digits = 3 + 1 + 2 + 5 + 6 = 17. 17 ÷ 3 = 5.67 (not divisible)

53784: Sum of digits = 5 + 3 + 7 + 8 + 4 = 27. 27 ÷ 3 = 9 (divisible)

35718: Sum of digits = 3 + 5 + 7 + 1 + 8 = 24. 24 ÷ 3 = 8 (divisible)

Since 53784 is divisible by both 8 and 3, it is a multiple of 24.

Thus, the correct answer is C) 53784.