Question

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

• A. 36
• B. 144
• C. 151
• D. 137

Answer 1

The correct option is C 151

To find the least number which is divisible by 12, 16 ,24 and 36, we need to find L.C.M. of these numbers.

$\begin{array}{cc}2& 12,16,24,36\\ 2& 6,8,12,18\\ 2& 3,4,6,9\\ 2& 3,2,3,9\\ 3& 3,1,3,9\\ 3& 1,1,1,3\\ & 1,1,1,1\end{array}$

L.C.M. of 12, 16, 24, 36 $=2\times 2\times 2\times 2\times 3\times 3=144$

Least Number which when divided by 12, 16 ,24 and 36 leaves a remainder 7 in each case $=144+7=151$