LCM of 7y^4 and 6w^2

To find the least common multiple (LCM) of 7y^4 and 6w^2, we need to first find the prime factorization of each term.

For 7y^4:
7 is a prime number.
y^4 can be written as (y^2)^2.

Therefore, the prime factorization of 7y^4 is 7 * (y^2)^2 = 7 * y^2 * y^2.

For 6w^2:
6 can be factored into 2 * 3.
w^2 can be written as w * w.

Therefore, the prime factorization of 6w^2 is 2 * 3 * w * w.

Now, we calculate the LCM by taking the highest power of each prime factor from the two factorizations:
LCM = 7 * y^2 * y^2 * 2 * 3 * w * w
LCM = 42y^2w^2

Therefore, the LCM of 7y^4 and 6w^2 is 42y^2w^2.