Question

The correct least number when divided by $12,16$ and $18$ leaves in each case a remainder $5$ is

• A. $149$
• B. $293$
• C. $337$
• D. $481$

Answer 1

Answer: (A)

$149$

Let that number be $x$

$\therefore x-5=LCM(12,16,18)$

$=LCM\left(LCM\right(12,16),18)$

for $LCM(12,16)$

$12=2\times 2\times 3$

$16=2\times 2\times 2\times 2$

$LCM=2\times 2\times 3\times 2\times 2$

$=48$

$LCM(48,18)$

$48=2\times 2\times 3\times 2\times 2$

$18=2\times 2\times 3$

$LCM=2\times 3\times 2\times 2\times 2\times 3$

$=144$

$\therefore x=144+5=149$