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02 Aug 2024, 09:49
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B
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Difficulty:
45%
(medium)
Question Stats:
58% (01:00) correct
42%
(01:11)
wrong
based on 90
sessions
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Is the least common postive multiple of positive integers x and y equal to the product xy?
(1) The LCM of x and y is 42.
(2) The GCD of x and y is 1
(1) The LCM of x and y is 42.
(2) The GCD of x and y is 1
Please help. Why not D and why B. [since With 1 it is proved that x and y LCM = xy]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
03 Aug 2024, 10:07
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S2930
Let's understand the question stem first: For any 2 positive integers' L.C.M. to be their product, the two integers have to be co-primes i.e. their GCD has to be 1.
Analyzing the statements now:-
(1) The LCM of x, y is 42.
We know 42 = 2*3*7 and for any two integers' LCM to be 42, we need prime factors 2, 3, 7. The pairs can be made up of only these prime factors taken once or twice:
Example: LCM of (6, 7), (3, 14) and (2, 21) is 42. Each pair is a pair of co-prime. Hence our answer: YES
Now, example: LCM of (6, 14) i.e. (2*3, 2*7) - [note '2' is taken twice] is also 42 where 6, 14 are not co-primes. Hence our answer: NO
We have two different answers, thus NOT SATISFACTORY.
(2) The GCD of x and y is 1.
Directly gives us what we need, hence SATISFACTORY
Hence our answer B.
03 Aug 2024, 18:51
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GCD means greatest common divisor/factor. If there are no common factors apart from 1, then we need to multiply both numbers to get LCM. So 2 alone is sufficient.
