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Rus_ich [418]
3 years ago
13

Find the LCM of 132 and 60 using Prime Factorization ?

Mathematics
1 answer:
Sav [38]3 years ago
4 0

Answer:

660

Step-by-step explanation:

First, let's find the prime factorization for both numbers.

132 = 11 x 12

12 = 3 x 4

4 = 2 x 2

<u>132 = 2 x 2 x 3 x 11</u>

60 = 5 x 12

12 = 3 x 4

4 = 2 x 2

<u>60 = 2 x 2 x 3 x 5</u>

Now, to find the lowest common multiple, we just need to multiply each number the most times it is seen in either number.

<u>132 = 2 x 2 x 3 x 11</u>

<u>60 = 2 x 2 x 3 x 5</u>

The first number is both is 2, which appears at most twice in either list so we will multiply two 2s to find the LCM.

Both numbers also have at most one 3, one 5, and one 11, so to find our LCM, we just need to multiply all these numbers together:

2 x 2 x 3 x 5 x 11 = 660

The LCM of 132 and 60 is 660.

Hope this helped!

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Find the measure of angles X and Y, as well as the values of x and y:
kotegsom [21]

Answer:

Step-by-step explanation:

By the Isosceles Triangle Theorem, if 2 sides of a triangle are congruent to each other, than the angles opposite those sides are also congruent. We see by the markings on the triangle that WX and WY are congruent. That means that angle Y (which is across from WX) and angle X (which is across from WY) are the same measure. We can set them equal to each other  because of this:

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But we have a problem because we have 2 unknowns.

Let's try this out: the Triangle Angle-Sum Theorem says that all the angles of a triangle have to add together to equal 180. That means that

52 + 6y - 2 + 4x + 20 = 180.

But we STILL have a problem with those 2 unknowns. BUT...

If angle X and angle Y are the same, then we don't need both 6y - 2 AND 4x + 20.  We only need 1 of those multiplied by 2 because they're the same measure. Changing things up a bit to reflect that:

52 + 2(4x + 20) = 180 and

52 + 8x + 40 = 180 and

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Let's check:

64 + 64 + 52 better equal 180. And it does, so we're good.

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4 years ago
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