What is the LCM of 12 and 16?

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#.

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#

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.