Find the smallest 4 digit number which is exactly divisible by 18, 24, 36.

Given:

18, 24 and 36.

To find:

We have to find the value of the least 4 digit number which is exactly divisible by 18, 24 and 36.

Solution:

We have to first find the LCM of 18, 24 and 36:

18 = 2 $\times$ 3 $\times$ 3

24 = 2 $\times$ 2 $\times$ 2 $\times$ 3

36 = 2 $\times$ 2 $\times$ 3 $\times$ 3

LCM = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 = 72

So, LCM of 18, 24 and 36 is 72. But we want the least 4 digit number, which is exactly divisible by 18, 24 and 36. 

Smallest 4 digit number = 1000.

Now,

1000 = (13 $\times$ 72) + 64

Next higher quotient is 14.

So, the required number = 14 $\times$ 72 = 1008

Hence, the required number is 1008, which is exactly divisible by 18, 24 and 36.

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Updated on: 10-Oct-2022

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