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# How many positive integers less than 100 are multiples of

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CEO
Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1075 [0], given: 4

Location: New York City
How many positive integers less than 100 are multiples of [#permalink]

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30 Oct 2007, 08:08
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many positive integers less than 100 are multiples of both 16 and 14?

0
1
2
3
4

How would you attack this question quickly?

Kudos [?]: 1075 [0], given: 4

Director
Joined: 11 Jun 2007
Posts: 909

Kudos [?]: 291 [0], given: 0

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30 Oct 2007, 08:14
bmwhype2 wrote:
How many positive integers less than 100 are multiples of both 16 and 14?

0
1
2
3
4

How would you attack this question quickly?

1) you can either write out the multiples of 14 and 16 (which didn't take me very long)

14, 28, 42, 56, 70, 84, 98
16, 32, 48, 64, 80, 96

OR

2) write out the prime factorization for both (again didn't take very long)
14 = 2*7
16 = 2*2*2*2
so the LCM = 2*2*2*2*7 = 16*7 = 112

nothing under 100, so 0

Kudos [?]: 291 [0], given: 0

Manager
Joined: 02 Aug 2007
Posts: 145

Kudos [?]: 51 [0], given: 0

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30 Oct 2007, 08:16
Got it

Get the prime factors of 16 & 14
16 = 2^4
14 = 2*7

Unique prime factors
so 2^4 * 7 = 112

A. Zero

Kudos [?]: 51 [0], given: 0

CEO
Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1075 [0], given: 4

Location: New York City

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31 Oct 2007, 08:45
beckee529 wrote:
bmwhype2 wrote:
How many positive integers less than 100 are multiples of both 16 and 14?

0
1
2
3
4

How would you attack this question quickly?

1) you can either write out the multiples of 14 and 16 (which didn't take me very long)

14, 28, 42, 56, 70, 84, 98
16, 32, 48, 64, 80, 96

OR

2) write out the prime factorization for both (again didn't take very long)
14 = 2*7
16 = 2*2*2*2
so the LCM = 2*2*2*2*7 = 16*7 = 112

nothing under 100, so 0

thanks. prime factorization is much quicker.

Kudos [?]: 1075 [0], given: 4

Re: LCM   [#permalink] 31 Oct 2007, 08:45
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# How many positive integers less than 100 are multiples of

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