Question

The smallest number, when it divided by $12,15,20$ and $54$, leaves a remainder of $6$ in each case is

• A. $534$
• B. $536$
• C. $542$
• D. $546$

Answer 1

The correct option is D $546$

The number will be
L.C.M. of $\{12,15,20,54\}+6$
L.C.M. of $\{12,15,20,54\}$
$12=2^2\times 3$
$15=3\times 5$
$20=2^2\times 5$
$12=2\times 3^3$
L.C.M. $=2^2\times 3^3\times 5=540$
Therefore, n​​​​​umber is $540+6=546$