GMATPrep GCF and LCM

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StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Sat Jan 26, 2008 5:29 pm

If n and t are positive integers, what is the greatest prime factor of nt?

1) The greatest common factor of n and t is 5.
2) The least common multiple of n and t is 105.

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Source: Beat The GMAT — Data Sufficiency | Sat Jan 26, 2008 5:29 pm

cris: Master | Next Rank: 500 Posts; Posts: 128; Joined: Sat Nov 17, 2007 11:59 am; Thanked: 1 times

by cris » Sat Jan 26, 2008 7:13 pm

I think is B. If I am corect I will explain :D

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malnv: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Wed Jan 16, 2008 9:10 pm

by malnv » Sat Jan 26, 2008 10:18 pm

Its C.

Number is LCM * GCF
prime factors for 105 *5 - 2,5,7

where 7 is greatest PF

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sankruth: Master | Next Rank: 500 Posts; Posts: 195; Joined: Sun Oct 21, 2007 4:33 am; Thanked: 10 times

by sankruth » Sun Jan 27, 2008 12:28 am

IMO the answer is B.

LCM will have all the unique prime factors of both numbers n & t, which will include the greatest prime factor.

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malnv: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Wed Jan 16, 2008 9:10 pm

by malnv » Sun Jan 27, 2008 12:43 am

You are right. LCM = product of highest power of ALL prime factors.
- B is SUFF

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StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Sun Jan 27, 2008 8:38 am

OA is B. I got it wrong though.

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