Which is the smallest 4-digit number divisible by 8, 10 and 12?

Given:

8, 10 and 12

To find:

We have to find the smallest 4-digit number divisible by 8, 10 and 12

Solution:

To find the smallest 4 digit number which is exactly divisible by 8, 10 and 12, we have to first find the LCM of 8, 10 and 12:

$8\ =\ 2\ \times \ 2\ \times \ 2$

$10\ =\ 2\ \times \ 5$

$12\ =\ 2\ \times \ 2\ \times \ 3$

LCM = 2 $\times $ 2 $\times $ 2 $\times $ 3 $\times $$\times$ 5 = 120

So, LCM of 8, 10 and 12 is 120. But we want the least 4 digit number, which is exactly divisible by 8, 10 and 12. 

Smallest 4 digit number = 1000.

Now,

$1000\ =\ ( 8\ \times \ 120) \ +\ 40$

Next higher quotient is 9.

So, the required number = 9 × 120 = 1080

Hence, the required number is 1080, which is exactly divisible by 8, 10 and 12.