Is the least common postive multiple of positive integers x and y

Question

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

Please help. Why not D and why B.

anmol8185 · Answer

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) -   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.

nagasatish · Answer

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.

Kinshook · Answer

@S2930Is the least common postive multiple of positive integers x and y equal to the product xy?

LCM(x,y) = xy if there is no common factor between x & y.

(1) The LCM of x and y is 42.
LCM(x,y) = 42 = 2*3*7
NOT SUFFICIENT

(2) The GCD of x and y is 1LCM(x,y)*GCD(x,y) = xy
LCM(x,y) = xy
SUFFICIENT

IMO B

Is the least common postive multiple of positive integers x and y

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Is the least common postive multiple of positive integers x and y