Find the smallest 5-digit number which is divisible by 12, 18, 30.

Given: Numbers 12, 18, 30.

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 $ \times $ 3 

18 = 2 $ \times $ 3² 

30 = 2 $ \times $ 3 $ \times $ 5 

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

LCM = 2² $\times$ 3²$\times$ 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 $\times$ 56 = 10080

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

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Updated on: 10-Oct-2022

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