Find the smallest number of six digits divisible by 18, 24 and 30

To find the smallest number of six digits divisible by 18, 24 and 30 we find the l.c.m. of them.

18 = 3 × 3 × 2

24 = 2 × 2 × 2 × 3

30 = 3 × 2 × 5

Therefore, l.c.m.(18, 24, 30) = 2 × 2 × 2 × 3 × 3 × 5 = 360

We know that the smallest six digit number is 100000.

Dividing 100000 by 18 = = 277. 77

So, the integer bigger and nearest to 277. 77 is 278.

Therefore, required integer = 278 × 360 = 100080

So, the smallest number of six digits divisible by 18, 24 and 30

is 100080.