Question

Which is the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case?

• A. 121
• B. 131
• C. 144
• D. 151

Answer 1

The correct option is D 151

The least number which is divisible by 12, 16, 24 and 36 is the LCM of 12, 16, 24 and 36.
12 = 2 $\times$ 2 $\times$ 3
16 = 2 $\times$ 2 $\times$ 2$\times$ 2
24 = 2 $\times$ 2 $\times$ 2 $\times$ 3
36 = 2 $\times$ 2 $\times$ 3 $\times$3
LCM of 12, 16, 24 and 36 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 = 144
Therefore, least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case = 144 + 7 = 151.