What is the LCM of 12 and 16?

3 Answers
Sep 28, 2016

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.

Sep 28, 2016

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

Sep 28, 2016

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.