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number properties from mgmat

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by rahul.s » Fri Feb 12, 2010 10:01 pm
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

(A) 140
(B) 210
(C) 1400
(D) 2100
(E) 3500

OA: D

i opted for the right answer choice, but after spending some time on it. is there a faster approach / method?
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by ajith » Fri Feb 12, 2010 10:17 pm
rahul.s wrote:Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

(A) 140
(B) 210
(C) 1400
(D) 2100
(E) 3500

OA: D

i opted for the right answer choice, but after spending some time on it. is there a faster approach / method?
The first five integer multiples of 5 are (5,10,15,20,25,30 and 35)
what is asked here is the LCM of 5,10,15,20,25,30 and 35
LCM of 5,10,15,20,25,30 and 35 =LCM of 10,15,20,25,30 and 35 =LCM of 60,20,25,30 and 35 = LCM of 60,25,30 and 35 = LCM of 300,30 and 35 = LCM of 300 and 35 = 2100
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by sanju09 » Sat Feb 13, 2010 12:40 am
rahul.s wrote:Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

(A) 140
(B) 210
(C) 1400
(D) 2100
(E) 3500

OA: D

i opted for the right answer choice, but after spending some time on it. is there a faster approach / method?
The first 7 positive integer multiples of 5 are 5, 10, 15, 20, 25, 30, and 35 and the lowest positive integer that is divisible by all of these is their lowest common multiple (also known as the LCM), which must be found out in its most conventional method in case it's hard to eyeball.

(5, 10, 15), (20, 25, 30), and 35

{(30), (300)}, 35

300, 35 (read 5 × 7)

300, 7

[spoiler]2100[/spoiler]

[spoiler]D[/spoiler]
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