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# The least possible value divisible by both a & b is 36. What are the v

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The least possible value divisible by both a & b is 36. What are the v  [#permalink]

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10 Oct 2018, 10:27
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Difficulty:

75% (hard)

Question Stats:

43% (02:33) correct 57% (01:27) wrong based on 29 sessions

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The least possible value divisible by both a & b is 36. What are the values of a & b?

(1) a is even and a prime factor of b
(2) GCD of a and b is 2
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Joined: 02 Aug 2009
Posts: 7334
Re: The least possible value divisible by both a & b is 36. What are the v  [#permalink]

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10 Oct 2018, 18:57
The least possible value divisible by both a & b is 36. What are the values of a & b?
Means LCM of a and b is 36

(1) a is even and a prime factor of b
Only one prime factor is even and that is 2 so a=2.
So b has to be 36 as any other number will give LCM as a smaller number.
Sufficient

(2) GCD of a and b is 2.
Numbers could be 4 and 18 or 2 and 36 and a and b could be any values of the two
Insufficient

A
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Re: The least possible value divisible by both a & b is 36. What are the v  [#permalink]

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10 Oct 2018, 19:20
LCM=36
Statement 1 ----- a is a prime factor and even. The only such prime no. is 2. We have the LCM and one number. This is enough to determine the other number. Its going to be 18. But, you dont need to calculate it. Sufficient

Stratement 2.

LCM*HCF/GCD = a*b
LCm is 36 HCF/GCD = 2 . therefore a*b= 72
We can have multiple values of a and b whose product is 72. Insufficient.
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Re: The least possible value divisible by both a & b is 36. What are the v   [#permalink] 10 Oct 2018, 19:20
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# The least possible value divisible by both a & b is 36. What are the v

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