Finding LCM?

Question

3a and 6a^2

Answer 1

6a^2 is the LCM

Answer 2

The way I like to find the LCM is to first
separate each term into their lowest factors.

3a = 3 * a
6a^2 = 2 * 3 * a * a

The LCM is the combination of the least amount of all these
factors such that both 3a and 6a^2 divide into it.

The least amount you can have as an LCM for 3a is 3 * a.
3 * a is therefore our LCM so far.

Looking at 6a^2, there is already a 3 * a in there,
and we know that 3a will divide into that.

But 6a^2 won't, unless you multiply it by the remaining 2 * a.

So the LCM for 6a^2 must be 2 * 3 * a * a = 6a^2.

We already know that 3a will divide into it.

So the final LCM must be 6a^2.

As another example :
Find the LCM of 16 and 24.

16 = 2 * 2 * 2 * 2,
so the final LCM has got to be at least 2 * 2 * 2 * 2.

24 = 2 * 2 * 2 * 3
We've already got those three 2's in 2 * 2 * 2 * 2.
But we haven't got the 3, so we have
to multiply that to our LCM so far.
This gives the final LCM as 2 * 2 * 2 * 2 * 3 = 48.
16 and 24 will now both divide into that.

Answer 3

The lowest common multiple is the biggest term that can be pulled out of both.

The trick to finding the lowest common multiple is to find the LCM of the numerical values first (the lcm of 3 and 6 is 6), and then the LCM of the variables. Whenever you compare variables (a and a^2), what you want to do is take the one with the higher power. In this case, it's a^2.

Therefore, the LCM of 3a and 6a^2 is 6a^2.

Applications of LCM: adding fractions.
Suppose we wanted to add the following:

1/(3a) + 1/(6a^2)

We need the lowest common denominator, which is the LCM of the denominators, and, as we calculated, is equal to 6a^2. So, we put both fractions under 6a^2,

1/(3a) = (2a) / (6a^2), so we end up adding

(2a) / (6a^2) + 1 / (6a^2), which we can merge as a single fraction with a common bottom,

(2a + 1) / (6a^2)

Answer 4

The least common multiple is the smallest number that both of your terms will divide evenly, without remainder. Since 3a divides 6a^2, and 6a^2 divides itself, the LCM would be 6a^2.
The LCM is always greater than or equal to the largest element of the set. It's what you'd use as the common denonminator if you were adding fractions.

Answer 5

6a^2 is the LCM, since 6a^2 is a multiple of both
3a (since 3a * 3a = 6a^2 ) and 6a^2 (6a^2 * 1).

Answer 6

That would be 6 a^2.

Answer 7

Rajaram has the right idea but thinks that 3a * 3a is 6a^2. Ha, ha. It's 9a^2.

The other answers are good.

Answer 8

H.C.F=Common Terms.
L.C.M=Biggest terms and L.C.M of the numbers.
=6a^2

Answer 9

3a and 6a^2
LCM=6a^2

Answer 10

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