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How many positive integers less than 80 are evenly divisible by 4, 5 a

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Bunuel
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How many positive integers less than 80 are evenly divisible by 4, 5 a [#permalink] How many positive integers less than 80 are evenly divisible by 4, 5 a   21 Jul 2020, 03:25
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How many positive integers less than 80 are evenly divisible by 4, 5 and 6?

A. 1
B. 2
C. 3
D. 4
E. 5
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A
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Re: How many positive integers less than 80 are evenly divisible by 4, 5 a [#permalink] How many positive integers less than 80 are evenly divisible by 4, 5 a   21 Jul 2020, 09:21
LCM of 4,5 and 6 = 60
So multiple of 60 are evenly divisive by 4,5&6

Among Number less than 80
60 is the only no. Which is divisivble by all 3 numbers, without leaving any remainder.
Hence answer should be A

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Re: How many positive integers less than 80 are evenly divisible by 4, 5 a [#permalink] How many positive integers less than 80 are evenly divisible by 4, 5 a   21 Jul 2020, 09:34
60 is divisible by 4,5,6. Which means only one positive integer below 80 is divisible by all.

Answer is A

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Re: How many positive integers less than 80 are evenly divisible by 4, 5 a [#permalink] How many positive integers less than 80 are evenly divisible by 4, 5 a   24 Jul 2020, 08:30
First, we need to perform a prime factorization:

4 = 2*2
5 = 5
6 = 3*2

To come up with the LCM, which is the least multiple that is divisible by all the three numbers in the set, we multiply all numbers together. For those numbers which are in common, such as two, we take it only from the number with the highest power.

2*2*5*3 = 60

60 is the only number below 80 which is divisible by all of the three given integers.
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Re: How many positive integers less than 80 are evenly divisible by 4, 5 a [#permalink]
24 Jul 2020, 08:30
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