Answer
$$2x\left(x+3\right)\left(x+7\right)$$
Work Step by Step
When the problem asks for the least common multiple, it is asking us for the smallest value that, when divided by either expression given, will result in a whole number. Finding the least common multiple using factors as well as trial and error, we find:
$$2x\left(x+3\right)\left(x+7\right)$$