Final answer:
The least common multiple (LCM) of 15w^4 and 9w^3 is found by determining the LCM of the numerical coefficients, 15 and 9, and taking the highest power of the variable w, which results in 45w^4. Therefore, the answer is option (a).
Step-by-step explanation:
To find the least common multiple (LCM) of 15w^4 and 9w^3, first identify the LCM of the numerical coefficients and the highest power of the variable present in both terms. The numerical coefficients are 15 and 9, while the variable terms are w^4 and w^3.
For the numerical coefficients, 15 can be factored into 3 × 5, and 9 can be factored into 3 × 3. The LCM will include each prime factor the greatest number of times it occurs in any of the numbers. Therefore, the LCM of 15 and 9 is 3 × 3 × 5 = 45.
For the variable w, we take the highest power, which is w^4, since w^4 includes w^3 within it.
Combining the LCM of the coefficients and the highest power of the variable, we get the LCM of 15w^4 and 9w^3 as 45w^4. Therefore, the answer is option (a).