Question

5. Find the smallest 3-digit number and the smallest 4-digit number, which are divisible
by 8, 6 and 9.​

Answer 1

Answer:

So the 14th multiple of 72 (that is 72×14 = 1008) will be the smallest 4-digit number divisible by 6, 8 and 9.

Explanation:

(1) Which is the smallest number divisible by 6, 8 and 9?

This is the LCM of 6, 8 and 9, i.e. 72. This is the smallest number which is divisible by 6, 8 and 9.

So, all numbers divisible by 6, 8 and 9 must be a multiple of 72 (144, 216, 288, 360…….).

(2) Now which multiple of 72 is the smallest 4-digit number?

Simply divide the smallest 4-digit number, 1000 by 72.

You will get 13 as quotient and 64 as remainder.

So the 14th multiple of 72 (that is 72×14 = 1008) will be the smallest 4-digit number divisible by 6, 8 and 9.