Question

What is the least common multiple of 8, 10, 12?

Answer 1

Least Common Multiple is `120`

Explanation:

Multiples of `8` are `{8,16,24,32,40,48,56,64,72,80,88,96,104,112,color(red)120,....}`

Multiples of `10` are `{10,20,30,40,50,60,70,80,90,100,110,color(red)120,....}`

Multiples of `12` are `{12,24,36,48,60,72,84,96,108,color(red)120,....}`

Hence common multiples are `{120,240,----}`

and Least Common Multiple is `120`

Answer 2

The general rule is to decompose the numbers into prime factors and then the lcm in the product of all factors raised to the highest power found in those numbers.

`8=2^3`

`10=2xx5`

`12=2^2xx3`

`lcm(8,10,12)= 2^3xx3xx5=120`