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DIVISILILITY Question

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Senior | Next Rank: 100 Posts
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by saege » Thu Apr 03, 2008 10:41 pm
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

1. 3500
2.2100
3.1400
4.210
5. 140

Hi guys does any know the method to solve this problem and the problems of similar type because I found the answer through a trial and method process of taking each answer and checking?

Does anyone have any other efficient method?
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by mandy12 » Thu Apr 03, 2008 11:44 pm
The problem simply asks for the LCM of (5,10,15,20,25,30,35) in a disguised way...

Now the LCM can be calculated as -

5*1, 5*2, 5*3, 5*2*2, 5*5, 5*2*3, 5*7

so the product of highest powers of each multiple are -

5^2 * 2^2*3^1*7^1 = 2100
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