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2 x 2 x 2 = 8

2 x 3 x 5 = 30

3 x 3 x 5 = 45

2 x 2 x 2 x 3 x 3 x 5 = 360, the LCM

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Q: What is the LCM of 8 30 45 using prime factorization?
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What is the LCM of 12 and 30 using prime factorization?

It is: 60


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To find the LCM of 12, 30, and 150, we need to decompose the numbers into their prime factors. The prime factorization of 12 is 2^2 * 3, the prime factorization of 30 is 2 * 3 * 5, and the prime factorization of 150 is 2 * 3 * 5^2. Now, we need to choose the common and uncommon prime factors with the highest exponent. The common prime factors are 2 and 3, and the uncommon prime factors are 5 and 2^2. Therefore, the LCM of 12, 30, and 150 is 2^2 * 3 * 5^2 = 300. [1]


What is the prime factorization of both the numerator and the denominator of the fraction?

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