Final answer:
The least common multiple (LCM) of 7x²y and 14w⁵x⁸y⁷ is 14w⁵x⁸y⁷, taking the largest coefficients and highest powers of variables present.
Step-by-step explanation:
To find the least common multiple of 7x²y and 14w⁵x⁸y⁷, we need to identify the highest powers of the variables and the largest coefficients present in both terms.
The least common multiple (LCM) of the numerical coefficients (7 and 14) is 14, since 14 is the smallest number that both 7 and 14 can divide into evenly.
For the variables, we take the highest powers of x and y that appear in either term. For x, the highest power is x⁸, and for y, it is y⁷. We do not factor in w when it's only in one of the terms. The variable w remains as w⁵.
Thus, the LCM of 7x²y and 14w⁵x⁸y⁷ is 14w⁵x⁸y⁷.