Question

The least number, which when divided by $12$, $15$, $20$ and $54$ leaves in each case a remainder of $8$ is:

• A. $504$
• B. $536$
• C. $544$
• D. $548$

Answer 1

Answer: (D)

$548$

The least number which when divided by $12,15,20$ and $54$ leaves remainder $8$ in each case is given by

$\text{L.C.M}(12,15,20,54)+8$

Now, we will calculate L.C.M of $12,15,20$ and $54$.

$12=2\times 2\times 3$

$15=3\times 5$

$20=2\times 2\times 5$

$54=2\times 3\times 3\times 3$

$\therefore$ L.C.M of $(12,15,20,54)=2\times 2\times 3\times 3\times 3\times 5=540$

So, Required number $=\text{L.C.M}(12,15,20,54)+8=540+8=548$

Hence, $\text{D}$ is the correct option.