What is the LCM for 4, 9, 12?

Question

Zoe Adams · Accepted Answer

Least Common Multiple is #36# Multiples of #4# are #{4,8,12,16,20,24,28,32,color(red)36,40,44,48,52,56,60,64,68,72...}# Multiples of #9# are #{9,18,27,color(red)36,45,54,63,72,81,90....}# Multiples of #12# are #{12,24,color(red)36,48,60,72,84,96,108,120,....}# Hence common multiples are #{color(red)36,72,----}# and Least Common Multiple is #color(red)36#

Skylar Adams · Answer

#LCM = 36#

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

Notice that you do not even need to consider #4#, because #4# is a factor of #12#, so any multiple of #12# will be a multiple of #4# as well.

#color(white)(............) 4 = 2xx2# #color(white)(............) 9 =color(white)(xxxx.x)3xx3# #color(white)(..........) 12 = 2xx2xx3# #color(white)(.................) darrcolor(white)(.)darrcolor(white)(m)darrcolor(white)(.)darr#

#LCM =" " 2xx2xx3xx3 = 36#

Notice that in factor form:

#2xx2# is there for the #4# #2xx2xx3# is there for the #12# #3xx3# is there for the #9#

All the numbers are in the LCM, but there are no unnecessary factors.

Roman Alvarez · Answer

Here's a fast and easy way to find LCMs and LCDs

Start with the largest figure. In this case, that is 12. You know that the LCM has to be some multiple of 12, so start considering the multiples of 12 one at a time. #12 xx 1# #larr# 12 doesn't work because 9 doesn't go into 12 evenly (even though 4 does.) #12 xx 2# #larr# 24 isn't it either because 9 doesn't go into 24 #12 xx 3# #larr# Here is the right answer. 4, 9, and 12 all go into 36 evenly ............................ Here's another example Find the LCM of 4, 6, and 10 Don't waste your time fooling around with prime factors. Instead, just rapidly consider each multiple of 10 until you hit on the one that works 10 -- thinking -- "Won't divide by 4 or 6" 20 -- thinking -- "Not divisible by 6" 30 -- thinking -- "Won't take 4" 40 -- thinking -- "Not divisible by 6" 50 ---thinking -- "Not divisible by 4 or 6" 60 -- #color(red)(Perfect!# This usually takes only a few seconds, and you should always do it this way when the numbers let you. If the numbers are too hard to work with like this, you can always just go back to finding prime factors again. But the first choice of the way to find LCMs and LCDs should be just thinking in turn about each multiple of the largest figure.

Gabriel Agustin · Answer

undefined The least common multiple (LCM) for 4, 9, and 12 is 36.