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Nonamiya
2 months ago
10

The LCM of three numbers is 7920 and their GCD is 12. Two of the numbers are 48 and 264. Using factor notation find the third nu

mber if one of its factors is 9.
Mathematics
1 answer:
Svet_ta [12.7K]2 months ago
6 0
The third number amounts to 180. To explain, let the third number equal 9x where x is an integer. The prime factorization of 48 is 2*2*2*2*3, while 264 equals 2*2*2*3*11. Then, 9x can be rewritten as 3*3*x, leading to 2*2*2*2*3*3*11*x equaling 7920y for some integer y. Thus, 1584x equals 7920y which simplifies to x = 7920y / 1584 = 5y. With the GCD being 12, x must include 4 as a factor. Since x is a multiple of 5, one possibility is 20, making y equal to 4. Hence, if x = 20, the third number becomes 9*20 = 180, which can be confirmed.
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step by step breakdown

Initially, we write:

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(

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3

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99

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(

324

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+

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