Architecture

Least Common Multiple Of 9 12 And 15, Methods To Find Lcm Of 9, 12, And 15

When we”re looking at the LCM (Least Common Multiple), we”re looking for a number that both 12 and 15 are a factor of. Oftentimes people simply assume that if we multiply the two together, we”ll find it. In this case, it”d be #12xx15=180#. 180 is a multiple of both, but is it the least one? Let”s look.

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I start with a prime factorization of both numbers:

#12=2xx2xx3#

#15=3xx5#

To find the LCM, we want to have all the prime factors from both numbers accounted for.

For instance, there are two 2s (in the 12). Let”s put those in:

#LCM=2xx2xx…#

There is one 3 in both the 12 and the 15, so we need one 3:

#LCM=2xx2xx3xx…#

And there is one 5 (in the 15) so let”s put that in:

#LCM=2xx2xx3xx5=60#

#12xx5=60##15xx3=60#

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sjc
Jan 30, 2018

#60#

Explanation:

another approach is to use teh relation

#ab=hcf(a,b)lcm(ab)#

now #hcf(12,15)=3#

#:.12xx15=3xxlcm(12,15)#

#lcm(12,15)=(cancel(12)^4xx15)/cancel(3)#

#lcm=4xx15=60#

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Meave60
Feb 1, 2018

The LCM is #60#.

Explanation:

The LCM is the least common multiple. We can find the LCM by listing the multiples of the two numbers and identifying the lowest multiple they have in common.

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#12:##12,24,36,48,color(red)60,72,84…#

#15:##15,30,45,color(red)60…#

The LCM is #60#.

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Parabola
Feb 1, 2018

#60#

Explanation:

Let”s try to find the LCM of #12# and #15#.

We get: #12=2*2*color(blue)3##15= color(blue)3*5#

We see that they both share #3# is their LCM.

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We divide each number by their LCM.

#12/3=>4#

#15/3=>5#

We multiply these two quotients and the LCM to get our final answer:

#3*4*5=60#

That is our answer!

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