Q: What is the least common multiple of 8x and 25y?

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The LCM of 8x and 25y is 200xy

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The two numbers are x2 - x and 8x - 4. The least common multiple is the product of the numbers divided by their greatest common factor. For this example, I will assume that x is a positive integer > 1, since otherwise x2-x = 0, and the least common multiple would then be 0. So, the next step is to determine the greatest common factor. To do that, factor each of the numbers. These numbers can be rewritten as x(x-1) and 4(2x-1). The factors of x2 - x are x and x-1. The factors of 8x - 4 are 2, 2, and 2x-1. Neither x nor x-1 evenly divide 2x-1. However, either x or x-1 is even, which means one of them is divisible by 2. Since 2 is a factor of 8x-4, the greatest common factor is at least 2, but since we do not know the value of x, the greatest common factor might be 4. So, the least common multiple is either (x2-x)(8x-4)/2 = (8x3-12x2-4x)/2 = 4x3-6x2-2x or (x2-x)(8x-4)/4 = (8x3-12x2-4x)/4 = 2x3-3x2-x.

I believe the GCF (Greatest Common Factor) would be 8x I believe the GCF (Greatest Common Factor) would be 8x

The GCF is 8x.

24

The GCF of 8x and 12x2 is 4x.

The GCF is 8x.

2x