Find the least common multiple BETWEEN TWO EXPRESSIONS

Question

Find the least common multiple of these two expressions

20x⁴y⁸ And 8u²x⁶y⁵

Answer 1

First factor each expression completely.

20(x^4)(y^8) = (2)(2)(5)(x)(x)(x)(x)(y)(y)(y)(y)(y)(y)(y)(y)

8(u^2)(x^6)(y^5) = (2)(2)(2)(u)(u)(x)(x)(x)(x)(x)(x)(y)(y)(y)(y)(y)

The LCM is found by taking the most number of each factor from each expression.

LCM = (2)(2)(2)(5)(u)(u)(x)(x)(x)(x)(x)(x)(y)(y)(y)(y)(y)(y)(y)(y) = 40(u^2)(x^6)(y^8)

Answer 2

For all the algebraic terms, just use all the variables to the highest power. For the constant terms include the highest power of each of the prime factors:

20 = 2²*5 8 = 2³ LCM = 2³*5 = 40

variable terms are x⁶y⁸u²

so, 40x⁶y⁸u²

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