Find the least number which when divided by 6, 15, and 18 leave a remainder of 5 in each case.

When a least number is completely divisible by a set of numbers, it is known as the 'Lowest Common Multiple' for those numbers.

Answer: The least number, which when divided by 6, 15, and 18 leave a remainder of 5 in each case, is 95.

A least or lowest common multiple is the smallest common multiple for a given set of numbers.

Explanation:

Let's list out the multiples for the given numbers.

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, ... , and so on.

Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, ... , and so on.

Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, ... , and so on.

Now the least common multiple of 6, 15, and 18 is 90.

So 90 is the least number which is completely divisible by 6, 15, and 18.

To find the least number which when divided by 6, 15, and 18 leaves a remainder of 'k' in each case:

We will have to add 'k' to the least common multiple.

So, the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case = 90 + 5 = 95

Therefore, the least number is 95.