Question

Find the least number, which when divided by 12, 15, 20 and 54 leaves a remainder of 8 in each case.

• A. 548
• B. 348
• C. 644
• D. 484

Answer 1

The correct option is A 548

We have to find the L.C.M of 12, 15, 20 and 54
The prime factor of $12=2\times 2\times 3=2^2\times 3$
The prime factor of $15=3\times 5$
The prime factor of $20=2\times 2\times 5=2^2\times 5$
The prime factor of $54=2\times 3\times 3\times 3=2\times 3^3$
L.C.M = Product of each prime factor with highest index used.
$=2^2\times 3^3\times 5=540$
The required number $=(540+8)=548$