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# Each of the two positive integers X and Y has exactly 3 distinct prime

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1443
Location: India
Each of the two positive integers X and Y has exactly 3 distinct prime  [#permalink]

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21 Mar 2019, 22:33
2
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Difficulty:

75% (hard)

Question Stats:

23% (03:21) correct 77% (02:56) wrong based on 12 sessions

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Each of the two positive integers X and Y has exactly 3 distinct prime factors. Least Common Multiple of X and Y has 5 distinct prime factors. X is divisible by 35 while Y is divisible by 33. Also X and Y are both even numbers, and neither of them is divisible by 4. On writing either X or Y in prime factorised form, it is observed that neither of them has a prime number with a power greater than 2. If the least common multiple of X & Y is denoted as N, then how many values of N are possible?

A. 16
B. 12
C. 10
D. 8
E. 4
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Joined: 02 Aug 2009
Posts: 7684
Re: Each of the two positive integers X and Y has exactly 3 distinct prime  [#permalink]

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22 Mar 2019, 07:45
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amanvermagmat wrote:
Each of the two positive integers X and Y has exactly 3 distinct prime factors. Least Common Multiple of X and Y has 5 distinct prime factors. X is divisible by 35 while Y is divisible by 33. Also X and Y are both even numbers, and neither of them is divisible by 4. On writing either X or Y in prime factorised form, it is observed that neither of them has a prime number with a power greater than 2. If the least common multiple of X & Y is denoted as N, then how many values of N are possible?

A. 16
B. 12
C. 10
D. 8
E. 4

So X is divisible by 35, that is 5*7, and X is even, so divisible by 2, thus $$X=2*5^{a}*7^{b}$$.. power of 2 is just 1 as the number is not divisible by 4...
Also, Y is divisible by 33, that is 3*11, and Y is even, so divisible by 2, thus $$X=2*3^{c}*11^{d}$$.. power of 2 is just 1 as the number is not divisible by 4...

LCM = $$2*3^c*5^a*7^b*11^d$$... Here a, b, c and d can take any of the two values, 1 or 2. Thus ways = 1*2*2*2*2=16

A
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Re: Each of the two positive integers X and Y has exactly 3 distinct prime   [#permalink] 22 Mar 2019, 07:45
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