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Least Common Multiple with Expressions

Let's find the least common multiple of x plus 5 squared, and 2 times x plus 5, and 6x. In order to do this we must go ahead and put each one as its prime factorization. So, x plus 5 squared is just simply x plus 5 times x plus 5. 2 times x plus 5 is exactly how it reads 2 times x plus 5, whereas 6x has three prime factors, 2 times 3 times x. Once again, we move left to right placing the missing primes into the LCM. So looking at this first one, this x plus 5 squared, we’re just simply going to place x plus 5 times x plus 5 into the LCM. Now that we are done with that we can go ahead and move onto this two times x plus 5. Notice, one of the x plus 5's are already in there, so the only thing we are concerned with is placing the 2. Now that we're done with the 2 times (x plus 5), we now look at this 6x. Notice there is a 2 already in there so we discard that and put in the 3 times x. Multiplying all of this together, we simply get 6 times x times x plus 5 squared.

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