What is the least common multiple of 12x and 40y?

The least common multiple is 2

Answered by brownbr1 | 2024-06-10

The least common multiple (LCM) of 12x and 40y is 120xy, which is found by taking the highest powers of all prime factors present in both numeric coefficients and accounting for the variables x and y.

The question asks us to find the least common multiple (LCM) of 12x and 40y. The LCM of two algebraic expressions is the smallest expression that both original expressions can divide into without leaving a remainder. To find the LCM, we need to factor both expressions and then take the highest powers of all the factors involved.
First, we factor the numeric coefficients: 12 = 22 times 3 and 40 = 23 times 5. Next, we identify the unique variables: x and y. Since we want the least common multiple, we take the highest powers of each prime factor present in both numbers. For the numeric part, we need a 23 (because that is the higher power of 2 between 22 and 23) and one factor of 3 and one factor of 5.
Thus, the LCM of 12x and 40y is 23 times 3 times 5 times x times y = 120xy.

Answered by qwarrow | 2024-06-24

The least common multiple of 12x and 40y, after factoring each term and taking the highest powers of their prime factors, is 120xy.
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Answered by brownbr1 | 2024-12-26