Question

what is the smallest 5digit number that is exactly divisible by 72and 108?

Answer 1

Let us find the LCM of 72 and 108, first

72 = 2x2x2x3x3

108 = 2x2x3x3x3

LCM is 2x2x2x3x3x3 = 216.

Next divide 10000 by 216 to get 46.296.

So the smallest five digit number divisible by 72 and 108 is 47*216 = 10152.

Answer 2

Answer:

Required 5-digit number is 10152.

Step-by-step explanation:

Given numbers are 72 and 108.

To find Smallest 5-Digit number divisible by 72 and 78.

First we find the LCM of 72 and 108,

Prime factorization,

72 = 2 x 2 x 2 x 3 x 3

108 = 2 x 2 x 3 x 3 x 3  

LCM = 2 x 2 x 2 x 3 x 3 x 3 = 216.

Now, To find Required 5-digit number we divide 10000 by 216.

On division we get,

Quotient =  46

Remainder = 64

So, the smallest five digit number divisible by 72 and 108 =  47 × 216 = 10152

Therefore, Required 5-digit number is 10152.