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Find the greatest common factor and the least common multiple of the following terms. Submit all

solution steps and your final answers to earn full credit.
8a³b5
16a²b7

User Sjmeverett
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Answer:

To find the greatest common factor, we need to find the largest factor that divides both terms evenly. We can factor each term as follows:

8a³b5 = 2³ * a³ * b5

16a²b7 = 2⁴ * a² * b7

The greatest common factor is the product of the lowest exponent of each prime factor that appears in both terms. Therefore, the greatest common factor is:

GCF = 2³ * a² * b5 = 8a²b5

To find the least common multiple, we need to find the smallest multiple that both terms share. We can start by writing out the prime factorization of each term:

8a³b5 = 2³ * a³ * b5

16a²b7 = 2⁴ * a² * b7

The least common multiple is the product of the highest exponent of each prime factor that appears in either term. Therefore, the least common multiple is:

LCM = 2⁴ * a³ * b7 = 16a³b7

So, the greatest common factor is 8a²b5 and the least common multiple is 16a³b7.

User Cube Drone
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