Question

determine the smallest 3 digit number which is exacctly divisible by 6,8and12.

Answer 1

first we have to find ,smallest number,who is divisible by 6,8,12 by using l.c.m
l.c.m of 6,8,12 = 24
there 24*2,24*3,24*4,and 24*5 are also divisible by 6,8,12
but 24*2=48, 24*3=72 ,24*4=96 are two digit numbers ,so smallest no. ,divisible by 6,8,12 =24*5=120

Answer 2

Break down each factor to its prime factors.



You need to keep the max exponent for each prime factor.
The lowest common factor would be ......

We need to find the common factor greater than 99.
Multiplying by 4 would only reach 96. 
Multiply by 5.

"which is the smallest 3 digit number which is exactly divisible by 6,8, 12"
120