Question #8c080

1 Answer
The Lonely Donut
Feb 12, 2017

# 12 #

Explanation:

To find the LCM of two numbers (or any amount of numbers) we must first find the prime factorization of each number separately.

Let's take the number # 4 #:

# 4 = 2 * 2 #

# 4 = 2^2 #

Now the number # 6 #:

# 6 = 2 * 3 #

From here we must determine the factors of each number with the highest exponent.

For example, both the number # 4 # and the number # 6 # share the factor # 2 #. But # 2 # appears twice in the prime factorization of # 4 #. So we must use that. We now have:

# 2^2 #

Another factor that appears is the number # 3 #. # 3 # only appears in the prime factorization of # 6 #, so we must use that. Now we have:

# 2^2 * 3 #

Simplify from here.

# 4 * 3 #

# 12 #

So therefore, the LCM of # 4 # and # 6 # is # 12 #.

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