Question

Find the smallest 4-digit number which is divisible by 6, 8, 9

Answer 1

Step-by-step explanation:

1. Ans. 1008
2. (1) Which is the smallest number divisible by 6, 8 and 9?
3. 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.
4. So, all numbers divisible by 6, 8 and 9 must be a multiple of 72 (144, 216, 288, 360…….).
5. (2) Now which multiple of 72 is the smallest 4-digit number?
6. Simply divide the smallest 4-digit number, 1000 by 72.
7. You will get 13 as quotient and 64 as remainder.
8. So the 14th multiple of 72 (that is 72×14 = 1008) will be the smallest 4-digit number divisible by 6, 8 and 9.