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If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple

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Joined: 02 Sep 2009
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If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple  [#permalink]

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New post 22 Aug 2018, 23:25
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

84% (01:34) correct 16% (01:00) wrong based on 31 sessions

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Joined: 11 Aug 2018
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Re: If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple  [#permalink]

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New post 22 Aug 2018, 23:35
1
i think it must have factor of 5 in it as well
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Re: If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple  [#permalink]

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New post 22 Aug 2018, 23:50
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If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple  [#permalink]

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New post 22 Aug 2018, 23:54
Bunuel wrote:
If \((2^a)(3^b)(5^c) = 3,240,000\), then what is the least common multiple of a, b, and c ?

A. 3
B. 6
C. 12
D. 16
E. 24


Prime factorizing \(3,240,000=(2^6)(3^4)(5^4)\)

Given, \((2^a)(3^b)(5^c) = 3,240,000\)
Or, \((2^a)(3^b)(5^c) =(2^6)(3^4)(5^4)\)
Or, a=6, b=4, c=4

LCM(a,b,c)=LCM(6,4,4)=12

Ans. (C)
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Re: If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple  [#permalink]

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New post 23 Aug 2018, 00:45
Prime factorisation of 3240000=2^6 X 3^4 X5^4
A/C, 2^a X 3^b X 5^c = 2^6 X 3^4 X5^4
Therefore, a=6, b=4, c=4
LCM (6,4,4)= 12
Ans.12 (c)
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If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple  [#permalink]

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New post 23 Aug 2018, 14:44
1
Bunuel wrote:
If \((2^a)(3^b)(5^c) = 3,240,000\), then what is the least common multiple of a, b, and c ?

A. 3
B. 6
C. 12
D. 16
E. 24



First Factorize 3240000

\(324 = 2^23^4\)

10000 = 100 * 100

= \(2^25^22^25^2\)

= \(2^4 5^4\)

324 * 10000 = 3240000

= \(2^23^4 * 2^45^4\)

= \(2^65^43^4\)

Least common multiple of a ,b, c = 6 , 4 , 4. = 12.

The best answer is C.
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If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple &nbs [#permalink] 23 Aug 2018, 14:44
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