Question

determine the smallest 3 digit number which is exactly divisible by 6 8 and 12

Answer 1

LCM of 6,8,12 is 24
the smallest 3 digit no. that can be divided by 6,8,12 will also be divided by 24
=>24×4=96
=>(24×5=120) ----3 digit no.
so 120 is the smallest 3 digit no.
i.e. closest to 100 and of 3 digits

Answer 2

Break down each factor to its prime factors.

6 = 2*3

8 = 2*2*2

12 = 2*2*3

Therefore the LCM of 6, 8, 12 = 24

We need a three digit number, therefore multiply 24 with natural numbers.

When we multiply 24 with 2, 3, 4 we get only 2 digits.

Therefore multiply 24 with 5.

Now we get the three digit number 120.

Therefore 120 is the smallest three digit number divisible by 6, 8 and 12.

Hope this helps you :)