# How do you find the LCM for #3#, #4w+2# and #4w^2-1#?

One way is to factor each of them completely, then multiply the non-duplicated factors together. I say non-duplicated, but if a factor is repeated in one of the factorisations of the starting expressions, then it has to occur at least that many times in the LCM.

Anyway:

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To find the least common multiple (LCM) for 3, 4w+2, and 4w^2-1, we need to factorize each expression and then determine the highest power of each factor that appears in any of the expressions.

The prime factorization of 3 is 3. The prime factorization of 4w+2 is 2(2w+1). The prime factorization of 4w^2-1 is (2w+1)(2w-1).

Now, we consider the highest power of each factor:

- The highest power of 2 is 2.
- The highest power of 3 is 1.
- The highest power of (2w+1) is 1.
- The highest power of (2w-1) is 1.

Multiplying these highest powers together, we get: 2^2 * 3^1 * (2w+1)^1 * (2w-1)^1

Simplifying this expression, the LCM for 3, 4w+2, and 4w^2-1 is: 12(2w+1)(2w-1)

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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