Question

Twe
Hence, the required
Find the smallest number of five digits which is exactly divisible by
12, 18, 24, 27 and 30.​

Answer 1

To find: Here we have to find the smallest 5-digit number which is divisible by 12, 18, 30.

Solution:

Let us find LCM of 12, 18, 30.

12 = 22 3

18 = 2 32

30 = 2 3 5

Multiply each factor the greatest number of times it occurs in all numbers:

LCM = 22 32 5

LCM = 180.

If a number is divisible by 12, 18, 30. Then it should be a multiple of 180.

So we need to find the small 5-digit number which is a multiple of 180.

The smallest 5-digits number is 10000.

Let us divide it by 180.

We get a quotient 55 remainder is 100.

If we add 80 to it then it will be completely divided by 180 with a quotient 56.

Therefore,

180 56 = 10080

So, smallest 5-digits number divisible by 12, 15, and 18 is 10080.