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Re: If M is the least common multiple of 90,196, and 300, which of the fol [#permalink]
1
SivhHarish wrote:
Well... i didn't even understand the first step even
A detailed explanation would be appreciated.


I've added a lot more to my original solution to show how I found the least common multiple.

Does that help?
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If M is the least common multiple of 90,196, and 300, which of the fol [#permalink]
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Given that M is the least common multiple of 90,196, and 300 and we need to find which of the following is NOT a factor of M

Lets find the value of M first

90 = 2*3*3*5 = \(2^1 * 3^2 * 5^1\)
196 = 4*49 = \(2^2 * 7^2\)
300 = 2*2*3*5*5 = \(2^2 * 3^1 * 5^2\)

To find the LCM take all the terms and take their highest power in all of the above.

=> M = LCM(90, 196, 300) = \(2^2 * 3^2 * 5^2 * 7^2\) = 9 * 49 * 100
=> The Answer choices should divide the LCM

A. 600 Clearly, 600 is NOT a factor of the LCM as 600 = 6*100 and M = 9 * 49 * 100 and 9 * 49 is NOT DIVISIBLE by 6.
In exam we don't need to test further but I am solving to complete the solution.

B. 700 = 7 * 100. M = 441 * 100 and 9 * 49 = is divisible by 7 => POSSIBLE

C. 900 = 9 * 100. M = 441 * 100 and 9 * 49 is divisible by 9 => POSSIBLE

D. 2,100 = 21 * 100. M = 441 * 100 and 9 * 49 is divisible by 21 => POSSIBLE

E. 4,900 = 49 * 100. M = 441 * 100 and 9 * 49 is divisible by 49 => POSSIBLE

So, Answer will be A
Hope it helps!

To learn more about LCM and GCD watch the following videos



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Re: If M is the least common multiple of 90,196, and 300, which of the fol [#permalink]
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