Answer: LCM = 132
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Step-by-step explanation
I'll go over 3 methods to finding the LCM
The first method has us take a slight detour to find the GCF.
Write the prime factorization of each value
We see that 2 is the only common factor, so it is the GCF.
Then we multiply the two original values and divide by the GCF to get the LCM.
So,
LCM = (x*y)/GCF
LCM = (12*22)/2
LCM = 264/2
LCM = 132
Note: This trick works when working with two values only.
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The 2nd method will have us return back to the prime factorization
12 = 2*2*3
22 = 2*11
We have the unique primes of: 2, 3, and 11
The prime "2" shows up at most twice, 3 at most once, and 11 at most once. This would mean the LCM is 2*2*3*11 = 4*33 = 132
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Method number 3
List out the multiples of 12 and 22 until you find a common multiple.
I'll highlight the smallest common multiple in bold
- Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, ...
- Multiples of 22 are: 22, 44, 66, 88, 110, 132, 154, 176, ...
We see that 132 is the LCM.
There are likely other methods to finding the LCM.