Question

Find the least number which when divided by 12, 15, 18 and 24 leaves a remainder 5 in each case.

• A. 360
• B. 300
• C. 365
• D. 355

Answer 1

The correct option is C 365

The least number that is exactly divisible by 12, 15,18 and 24 is the LCM of the three numbers.

$\begin{array}{cc}2& 12,15,18,24\\ 2& 6,15,9,12\\ 2& 3,15,9,6\\ 3& 3,15,9,3\\ 3& 1,5,3,1\\ 5& 1,5,1,1\\ & 1,1,1,1\end{array}$

L.C.M. of 12, 16, 24, 36 $=2\times 2\times 2\times 3\times 3\times 5=360$

360 is the least number which when divided by the given numbers will leave remainder 0 in each case.

Therefore, the least number which when divided by 12, 15, 18 and 24 leaves a remainder 5 in each case = 360 + 5 = 365