Answer: Choice C. 7 and 8
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Step-by-step explanation
LCM = least common multiple
GCF = greatest common factor
Before we can find the LCM, we need the GCF.
Write the prime factorization of each given value.
Both have 2*2 = 4 in common, so this is the GCF.
We can now find the LCM.
LCM of x and y = (x*y)/(GCF of x and y) ....... see note below
LCM = (8*28)/4
LCM = 56
Note: This formula only works when dealing with 2 values. If you have a set of 3 or more values, then you'll need to do a slight work-around.
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We found the LCM of 8 and 28 is 56.
We can confirm this by listing multiples and then circling what they have in common. I'll mark the LCM in bold
- Multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, ...
- Multiples of 28 are: 28, 56, 84, 112, ...
This confirms we have the correct LCM.
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Use either technique to find the LCM of answer choices A through D.
- A. LCM = (16*20)/4 = 80
- B. LCM = (18*24)/6 = 72
- C. LCM = (7*8)/1 = 56, we found the answer
- D. LCM = (4*14)/2 = 28
Note that 56 is a common multiple of 4 and 14, but not the LCM.
I used the LCM command in GeoGebra to confirm the answer.