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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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Math Expert
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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23 Aug 2018, 00:25
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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

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Joined: 11 Aug 2018
Posts: 111
Location: Pakistan
GPA: 2.73
Re: If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple  [#permalink]

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23 Aug 2018, 00:35
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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23 Aug 2018, 00:50
alitariquet wrote:
i think it must have factor of 5 in it as well

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Edited. Thank you.
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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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23 Aug 2018, 00:54
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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23 Aug 2018, 01:45
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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23 Aug 2018, 15:44
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.

If (2^a)(3^b)(5^c) = 3,240,000, then what is the least common multiple   [#permalink] 23 Aug 2018, 15:44
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