Question

Find the least number which when divided by $12,16,24$and $36$ leaves a remainder $5$ in each case.

Answer 1

The smallest number is exactly divisible by $12,16,24,$ and $36$ = L.C.M.$(12,16,24,36)$

⇒ The smallest number which leaves $5$ as the remainder when divided by $12,16,24,$ and$36$ = LCM$(12,16,24,36)+5$

$12=2\times 2\times 3$
$16=2\times 2\times 2\times 2$
$24=2\times 2\times 2\times 3$
$36=2\times 2\times 3\times 3$

LCM$(12,16,24,36)=2\times 2\times 2\times 2\times 3\times 3=144$

⇒ The required number = $144+5=149.$