Question

Which of the following is the smallest number that leaves a remainder of 5 when divided by 7, 15, 16 and 21?

• A. 1500
• B. 1680
• C. 1600
• D. 1685

Answer 1

The correct option is D

1685

The smallest number that is exactly divisible by a set of numbers is the Lowest
Common Multiple of those numbers.

7= 1 $\times$ 7

15= 1 $\times$ 3 $\times$ 5

16= 1 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2

21= 1 $\times$ 3 $\times$ 7

LCM= 3 $\times$ 7 $\times$ 5 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2= 1680

1680 will leave a remainder 0 when divided by 7, 15, 16 and 21.

Thus, 1680+5= 1685 will leave a remainder 5.