# How do you find the LCM of #18xy^2, 15y^3#?

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To find the least common multiple (LCM) of two or more algebraic expressions, follow these steps:

- Factor each expression into its prime factors.
- Identify the highest power of each prime factor present in any of the expressions.
- Multiply these highest powers together to find the LCM.

For the given expressions (18xy^2) and (15y^3):

[ 18xy^2 = 2 \times 3^2 \times x \times y^2 ] [ 15y^3 = 3 \times 5 \times y^3 ]

Identifying the highest powers of each prime factor:

- Prime factor 2: ( 2^1 ) (present in (18xy^2))
- Prime factor 3: ( 3^2 ) (present in both (18xy^2) and (15y^3))
- Prime factor 5: ( 5^1 ) (present in (15y^3))
- Prime factor ( x ): ( x^1 ) (present in (18xy^2))
- Prime factor ( y ): ( y^3 ) (present in (15y^3))

Now, multiply the highest powers together to find the LCM:

[ LCM = 2^1 \times 3^2 \times 5^1 \times x^1 \times y^3 ] [ LCM = 2 \times 9 \times 5 \times x \times y^3 ] [ LCM = 90xy^3 ]

Therefore, the LCM of (18xy^2) and (15y^3) is (90xy^3).

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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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