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24 votes
24 votes
What numbers between 61 and 107 that is multiple of 5, 8, and 10?

User LeMoisela
by
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1 Answer

21 votes
21 votes

Answer: 80

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Step-by-step explanation:

We'll need to find the LCM of 5, 8 and 10.

List out the prime factorization of the three numbers.

  • 5 = 1*5
  • 8 = 2^3
  • 10 = 2*5

The unique prime factors are 2 and 5. The '1' isn't a prime number, so we can ignore it.

The '2' has an exponent of 3 as the largest exponent, meaning 2^3 is part of the LCM. The '5' has the largest exponent of 1. So 5^1 = 5 is also part of the LCM

LCM = 2^3*5 = 8*5 = 40

List out the multiples of 40

40, 80, 120, 160, ...

The number 80 is the only multiple between 61 and 107

User Volearix
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3.2k points