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pbanavara: Master | Next Rank: 500 Posts; Posts: 279; Joined: Wed Sep 24, 2008 8:26 am; Location: Portland, OR; Thanked: 6 times

by pbanavara » Thu Jan 08, 2009 10:11 pm

k is a positive integer and 225 and 216 are both divisors of k. If k= 2^a*3^b*5^c , where a, band c
are positive integers, what is the least possible value of a+ b+ c

225 * 216 = 15^2 * 6^3 = 5^2 *3^2 * 2^3 * 3^3
= 5^2 *3^5*2^3

So a+b+c = 10. What's wrong with this ?

- pradeep

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Source: Beat The GMAT — Problem Solving | Thu Jan 08, 2009 10:11 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Thu Jan 08, 2009 10:26 pm

When u r multiplying them u r basically finding the min(a+b+c) for the product.

U may need to consider them individually since aLl it says that number has both 225 and 216 as its divisors/factors. With this constarint we have to find min(a+b+c)

225 = 5^2 * 3^2

216 = 2^3 * 3^3

min(a+b+c) for that number is 5^2 + 2^3 + 3^3

2+3+3 = 8

Hope this helps!

Regards,
CR

amitabhprasad: Master | Next Rank: 500 Posts; Posts: 259; Joined: Thu Jan 18, 2007 8:30 pm; Thanked: 16 times

by amitabhprasad » Thu Jan 08, 2009 10:26 pm

Question asked for least.
and Least will be LCM of 225 and 216
= 5^2*3^3*2^3
so a+b+c = 8.
I hope thats the right answer....

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Thu Jan 08, 2009 10:30 pm

Amit said it right! LCM would be oneway to look at this problem.

Either u can split the prime factors powers individually for both numbers or find the LCM and break it in to prime factors powers, like Amit did.

pbanavara: Master | Next Rank: 500 Posts; Posts: 279; Joined: Wed Sep 24, 2008 8:26 am; Location: Portland, OR; Thanked: 6 times

by pbanavara » Thu Jan 08, 2009 10:39 pm

Yep it's 8 thanks guys - Guess I should hit the bed .. LOL - such silly mistakes

- pradeep

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