The aggregate number of whole numbers between 100 and 200 which are divisible…

A whole number that is divisible by two given numbers together must be divisible by their Least Common Multiple (LCM). So, to count how many integers in a range are divisible by both of two numbers, first find the LCM of the two numbers, then count the multiples of that LCM lying inside the range.

1. Find the LCM of 9 and 6. Since 9 = 32 and 6 = 2 × 3, the LCM is 2 × 32 = 18.

2. List the multiples of 18 that lie between 100 and 200: 108, 126, 144, 162, 180, and 198.

3. Count the numbers in this list: there are 6 multiples of 18 between 100 and 200.

As an independent check, use the multiple-counting formula: the number of multiples of 18 up to 200 is ⌊200 ÷ 18⌋ = 11, and the number of multiples of 18 up to 100 is ⌊100 ÷ 18⌋ = 5. The count of multiples of 18 strictly between 100 and 200 is therefore 11 − 5 = 6, which matches the list above. Each listed number can also be checked directly — for example, 108 ÷ 9 = 12 and 108 ÷ 6 = 18, both whole numbers, confirming it is divisible by both 9 and 6.

So, the aggregate number of whole numbers between 100 and 200 that are divisible by both 9 and 6 is 6.