Answer: 24
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There are 3 methods to find the lowest common multiple (LCM)
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Method 1
List out the multiples of 6 and 8
multiples of 6 = {6, 12, 18, 24, 30, 36, 42, 48, ...}
multiples of 8 = {8, 16, 24, 32, 40, 48, ...}
We see that 24 is the smallest number in both sets at the same time. So this is the LCM.
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Method 2
Write the prime factorization of 6 and 8
prime factorization of 6 = 2*3
prime factorization of 8 = 2*2*2
The unique prime factors here are 2 and 3. We have 2 show up at most three times meaning that 2*2*2 = 8 is a factor of the LCM. The number 3 is also a factor meaning that 8*3 = 24 is the LCM.
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Method 3
Multiply the denominators 6 and 8 to get 6*8 = 48
48 is a common multiple, but its not the smallest
we can divide 48 over the GCF 2 to get 48/2 = 24, which is the actual LCM.
So when you have 2 different denominators, you can multiply their values and then divide by the GCF to get the LCM.