Question

The least multiple of 7 which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is ___.

• A. 74
• B. 94
• C. 184
• D. 364

Answer 1

The correct option is D

364

We first find the L.C.M of 6, 9, 15 and 18, which is 90.

For getting remainder 4, we need to add 4 to it.
i.e., 90 +4 = 94.

But, 94 is not divisible by 7. So, we proceed with the next multiple of 90, which is 180.

Adding 4 to 180, we get 184, which is also not divisible by 7.

The next multiple of 90 is 270.

Adding 4 to 270, we get 274, again not divisible by 7.

The next multiple of 90 is 360.

Adding 4 to it gives us 364, divisible by 7( as $\frac{364}{7}=52$).

Hence, the answer is 364.