Question

Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.

Answer 1

The least common multiple (LCM) of 2 or more numbers is the smallest number that they all divide evenly.

LCM:

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

LCM of 6, 15 and 18 = $2\times 3\times 3\times 5$ = 90
Therefore, the required number = 90 + 5 = 95 [Since 5 is the remainder in each case]