If the least common multiple of positive integer m and n is 120, and m:n=3:4, what is the greatest common factor of m and n?
(A) 3
(B) 5
(C) 6
(D) 10
(E) 12
The OA is the option D.
I don't know how can I solve this PS question. Is there a formula or something? Please, someone, help me.
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If the least common multiple of positive integer
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Shahrukh_mbabreakspace
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Since m and n are in ratio 3:4, let us assume them to be 3x and 4x
So, now hcf of 3x and 4x is obviously x
Formula is hcf * lcm= product of two number
x*120= 3x*4x
so x=10
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B.Tech IIT Roorkee
So, now hcf of 3x and 4x is obviously x
Formula is hcf * lcm= product of two number
x*120= 3x*4x
so x=10
________________________________________
Shahrukh Moin Khan
QA Mentor at Breakspace
https://www.mbabreakspace.com
PGDM: IIM Calcutta
B.Tech IIT Roorkee
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Hi VJesus12,
We're told that the least common multiple of positive integers M and N is 120 and M:N=3:4. We're asked for the greatest common factor of M and N. If you don't immediately see how to best approach a question, then you should consider 'brute force' - so you can then define what patterns are involved and get to the correct answer without spending too much time 'staring' at it.
Since M and N are in the ratio of 3 to 4, the two values could be....
M=3 and N=4. In this situation, the least common multiple would be 12 (re: 3x4 and 4x3)
M=6 and N=8. In this situation, the least common multiple would be 24 (re: 6x4 and 8x3)
M=9 and N=12. In this situation, the least common multiple would be 36 (re: 9x4 and 12x3)
At this point, you should recognize that the multiples follow a pattern: You'll need to multiply M by 4 and N by 3 to get the least common multiple. The prompt tells us that the LCM is supposed to be 120, so M and N must be....
M=30 and N=40
From here, you can find the Greatest Common Factor:
Factors of 30: 1&30, 2&15, 3&10, 5&6
Factors of 40: 1&40, 2&20, 4&10, 5&8
The GCF is 10
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're told that the least common multiple of positive integers M and N is 120 and M:N=3:4. We're asked for the greatest common factor of M and N. If you don't immediately see how to best approach a question, then you should consider 'brute force' - so you can then define what patterns are involved and get to the correct answer without spending too much time 'staring' at it.
Since M and N are in the ratio of 3 to 4, the two values could be....
M=3 and N=4. In this situation, the least common multiple would be 12 (re: 3x4 and 4x3)
M=6 and N=8. In this situation, the least common multiple would be 24 (re: 6x4 and 8x3)
M=9 and N=12. In this situation, the least common multiple would be 36 (re: 9x4 and 12x3)
At this point, you should recognize that the multiples follow a pattern: You'll need to multiply M by 4 and N by 3 to get the least common multiple. The prompt tells us that the LCM is supposed to be 120, so M and N must be....
M=30 and N=40
From here, you can find the Greatest Common Factor:
Factors of 30: 1&30, 2&15, 3&10, 5&6
Factors of 40: 1&40, 2&20, 4&10, 5&8
The GCF is 10
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Scott@TargetTestPrep
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We can let m = 3x and n = 4x for some positive integer x. We see that since 3 and 4 have no common factor (other than 1), the least common multiple (LCM) of m and n must be (3)(4)(x). Since it's given that the LCM is 120, we have:VJesus12 wrote:If the least common multiple of positive integer m and n is 120, and m:n=3:4, what is the greatest common factor of m and n?
(A) 3
(B) 5
(C) 6
(D) 10
(E) 12
(3)(4)(x) = 120
12x = 120
x = 10
So m = 30 and n = 40, and we see that 10 is the greatest common factor of m and n.
Answer: D
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