Question

Find the smallest 4 digit number which is exactly divisible by 6, 9 and 12.

Answer 1

Answer:

Hi Make sure to use LCM for fisding out the smallest digit number

Step-by-step 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.

Ans. 1008