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# 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 = 2^{2} $ \times $ 3

18 = 2 $ \times $ 3^{2}

30 = 2 $ \times $ 3 $ \times $ 5

__Multiply each factor the greatest number of times it occurs in all numbers__:

LCM = 2^{2} $\times$ 3^{2}$\times$ 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.