45 = 3 x 3 x 5
60 = 2 x 2 x 3 x 5
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No, 3x5x4 is not a prime factorization of 60. A prime factorization of 60 would consist of only prime numbers. The prime factorization of 60 is 2x2x3x5.
Prime factorization of 45 is 3x3x5. Prime factorization of 65 is 5x13.
The prime factorization of 50 is 2x5x5 or 2x52. The prime factorization of 60 is 2x2x3x5 or 22x3 x 5. The prime factorization of 300 is 2x2x3x5x5 or 22 x 3 x 52.
The prime factorization of 45 is 3 x 3 x 5. To find an LCM it is necessary to compare and combine that prime factorization with at least one other.
45 15,3 5,3,3