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m is a positive integer less than 300 and has exactly two e

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Joined: 18 Apr 2015
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Kudos [?]: 313 [0], given: 1278

m is a positive integer less than 300 and has exactly two e [#permalink] New post 09 Aug 2017, 15:26
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m is a positive integer less than 300 and has exactly two even and two odd prime factors in its prime factorization. What is the maximum possible value of m ?

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[Reveal] Spoiler: OA
276

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Joined: 17 Feb 2017
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Kudos [?]: 5 [0], given: 18

Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post 30 Aug 2017, 08:33
any explanation??
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Kudos [?]: 313 [0], given: 1278

Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post 31 Aug 2017, 09:03
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Because the only even prime number is 2, m must be the product of 2 × 2 = 4 and two odd primes. Further, due to the restriction that m be less than 300, the product of those two odd primes must be less than \frac{300}{4} = 75. Thus, you need to find the largest number smaller than 75 that is the product of exactly two odd prime numbers. You can rule out even numbers, and you have 73, which is prime, as is 71; 69 is the product of two prime numbers (3 and 23). Thus, the maximum possible value for m is 2 × 2 × 3 × 23 = 276.


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Re: m is a positive integer less than 300 and has exactly two e   [#permalink] 31 Aug 2017, 09:03
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