LCM of 6c^5b^4, 3c^5, b^5, 14c^8b^2

Question

LCM of: 6c^5b^4,3c^5,b6^5,14c68b^2

Answer 1

6c^5b^4 = 2 * 3 * c * c * c * c * c * b * b * b * b

3c^5 = 3 * c * c * c * c * c

6b^5 = 2 * 3 * b * b * b * b * b

14c^8b^2 = 2 * 7 * c * c * c * c * c * c * c * c * b * b

For the numbers we need 2 * 3 * 7 = 42 because we have to have something that 6, 3, 6, and 14 all go into.  We're building a pool of prime factors that each of the numbers (6, 3, 6, and 14) can be made from.

For the c's, we need c * c * c * c * c * c * c * c = c^8 because that's the smallest c thing we can make that all of the c's (c^5, c^5, and c^8) will go into.

For the b's we need b * b * b * b * b = b^5 because that's the smallest b thing we can make that all of the b's (b^4, b^5, b^2) will go into.

Answer:  42 c^8 b^5