determine the lowest common multiple of the following 4x2y2, 6xy, 10xy2&nbsp;

Question

determine the lowest common multiple of the following 4x2y2, 6xy, 10xy2&amp;nbsp;

nick1337 · Accepted Answer

To determine the lowest common multiple (LCM) of the given expressions, we need to factorize each of them into their prime factors. Then, we can find the product of all the prime factors with their highest power to get the LCM.
Let's factorize each expression:

4 x^{2} y^{2} = 2^{2} \cdot 2 \cdot x \cdot x \cdot y \cdot y = 2^{2} \cdot (x y)^{2}

6 x y = 2 \cdot 3 \cdot x \cdot y

10 x y^{2} = 2 \cdot 5 \cdot x \cdot y^{2}

Now, let's write the prime factorization of each expression in terms of their common factors, which are 2, x, and y:

4 x^{2} y^{2} = 2^{2} \cdot x \cdot y^{2} \cdot (x y)

6 x y = 2 \cdot 3 \cdot x \cdot y \cdot (1)

10 x y^{2} = 2 \cdot 5 \cdot x \cdot y^{2} \cdot (1)

We can see that the LCM should contain all the factors above with their highest power:

L C M = 2^{2} \cdot 3 \cdot 5 \cdot x \cdot y^{2} \cdot (x y)

Simplifying this expression, we get:

L C M = 60 x^{2} y^{3}

Therefore, the lowest common multiple of

4 x^{2} y^{2}

,

6 x y

, and

10 x y^{2}

is

60 x^{2} y^{3}

.

determine the lowest common multiple of the following

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