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# M14-14

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Math Expert
Joined: 02 Sep 2009
Posts: 49303

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16 Sep 2014, 00:53
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Difficulty:

25% (medium)

Question Stats:

76% (00:43) correct 24% (00:30) wrong based on 72 sessions

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

A. 0
B. 1
C. 2
D. 3
E. 4

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Math Expert
Joined: 02 Sep 2009
Posts: 49303

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16 Sep 2014, 00:53
Official Solution:

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

A. 0
B. 1
C. 2
D. 3
E. 4

For an integer to be divisible by both 16 and 14 it should be divisible by the least common multiple of $$16=2^4$$ and $$14=2*7$$ which is $$2^4*7=112$$. So, the least positive integer which is divisible by both 16 and 14 is 112, hence no integer less than 100 is a multiple of both 16 and 14.

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Joined: 02 Sep 2016
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23 Aug 2017, 04:56
Bunuel

In what all type of questions should we use LCM ? How will we know we are being asked to calculate LCM to get to the answer?
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Intern
Joined: 13 May 2013
Posts: 3
GMAT 1: 660 Q49 V31

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06 Sep 2017, 00:40
Hi Bunuel, If the question had been like mentioned below, would the answer be A? (because now the zero is also included) -

How many non negative integers less than 100 are multiples of both 16 and 14?
Math Expert
Joined: 02 Sep 2009
Posts: 49303

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06 Sep 2017, 00:42
Sandesh0476 wrote:
Hi Bunuel, If the question had been like mentioned below, would the answer be A? (because now the zero is also included) -

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

In this case the answer would be 1 (B) because 0 is a multiple of every positive integer.
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Intern
Joined: 13 May 2013
Posts: 3
GMAT 1: 660 Q49 V31

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06 Sep 2017, 02:43
Oh yes, correct. Thanks

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Re: M14-14 &nbs [#permalink] 06 Sep 2017, 02:43
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# M14-14

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