Question

What is the LCM of 12 and 16?

Answer 1

Least Common Multiple is `48`.

Explanation:

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

Multiples of `16` are `{16,32,color(red)48,64,80,color(red)96,112,...}`

Hence, common multiples are `{48,96,...........}`

and Least Common Multiple is `48`.

Answer 2

48

Explanation:

Consider the smaller of the 2 numbers, that is 12 and it's multiples. That is 12 times (2,3,4,5,6,7,8,9). When the larger number 16 divides exactly into one of the multiples of 12 then that is the LCM.

• Can 12 be divided exactly by 16 ? No - so not 12.

• Can 24 be divided exactly by 16 ? No - so not 24.

• Can 36 be divided exactly by 16 ? No-so not 36.

• Can 48 be divided exactly by 16 > Yes 3 times.

`rArr48 " is the LCM of " 12" and " 16`

Answer 3

`LCM = 2^4 xx 3 = 16 xx3 = 48`

Explanation:

Write each number as the product of its prime factors. Then you know what you working with.

`color(white)(xxxx)16 = 2xx2xx2xx2color(white)(xxxxxx) =2^4`
`color(white)(xxxx)12 = 2xx2color(white)(xxxxxx)xx3color(white)(xxx)= 2^2 xx3`

The LCM must be contain all of the prime factors, but without unnecessary duplicates.

`LCM = 2^4 xx 3 = 16 xx3 = 48`

This is the same method which is used in Algebra.