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# What is the lowest positive integer that is divisible by both 5,000,00

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What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

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15 Nov 2016, 10:10
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45% (medium)

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63% (01:31) correct 37% (01:33) wrong based on 107 sessions

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What is the lowest positive integer that is divisible by both 5,000,000 and 256?

A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000

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Re: What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

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15 Nov 2016, 10:24
1
Bunuel wrote:
What is the lowest positive integer that is divisible by both 5,000,000 and 256?

A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000

5,000,000= 5^1*10^6==> 5^7*2^6
256= 2^8
Required= LCM(5,000,000, 256)= 5^7*2^8 = 2*10^7
C

Alternate way
Both values of 5,000,000 and 256 must divide the values in the option

A. 5,000,000 ==== (5^7 * 2^6)/2^8 Not completely divisible
B. 10,000,000 === (5^7 * 2^7)/2^8 Not completely divisible
C. 20,000,000 === (5^7 * 2^8)/2^8 Divisible lowest positive integer
D. 50,000,000 === (5^8 * 2^7)/2^8 Not completely divisible
E. 100,000,000 === (5^8 * 2^8)/2^8 Divisible
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Re: What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

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15 Nov 2016, 10:26
Finding the Least Common Multiple of 256 and 5,000,000 gives 20,000,000.
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What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

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15 Nov 2016, 11:13
Bunuel wrote:
What is the lowest positive integer that is divisible by both 5,000,000 and 256?

A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000

$$5000000 = 2^6 * 5^7$$
$$256 = 2^8$$

Lowest positive integer that is divisible by both 5,000,000 and 256 = LCM of ( $$2^6 x 5^7 , 2^8$$ ) = $$2^6 * 5^7$$ = $$20,000,000$$

Hence, answer will be (C) $$20,000,000$$
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Re: What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

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17 Nov 2016, 14:44
Bunuel wrote:
What is the lowest positive integer that is divisible by both 5,000,000 and 256?

A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000

Taking a quick scan of our answer choices, we see that all answer choices are divisible by 5,000,000, so we really need to determine which of the answer choices is the smallest value divisible by 256.

Breaking 256 into primes, we see that 256 = 2^8. Thus, we need to find the smallest value that has 8 twos among the answer choices. Let’s start with answer A.

A) 5,000,000 = 5 x 1,000,000 = 5 x 10^6 = 5 x 5^6 x 2^6

Since 5,000,000 only has 6 twos, it is not divisible by 256.

B) 10,000,000 = 10^7 = 2^7 x 5^7

Since 10,000,000 only has 7 twos, it is not divisible by 256.

C) 20,000,000 = 2 x 10,000,000 = 2 x 10^7 = 2^1 x 2^7 x 5^7 = 2^8 x 5^7.

Since 20,000,000 has 8 twos, it’s divisible by 256, and thus, 20,000,000 is the lowest positive integer that is divisible by both 5,000,000 and 256.

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Re: What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

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04 Dec 2017, 12:46
256 has only eight 2's --> $$2^8$$

5,000,000 has six 0's and each zero = 5 x 2 --> therefore it has six 2's

There are therefore two 2's leftover from 256 that are not counted in 5,000,000, we simply have to multiply 5,000,000 by $$2^2$$
= 5,000,000 x 4 = 20,000,000
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Re: What is the lowest positive integer that is divisible by both 5,000,00 &nbs [#permalink] 04 Dec 2017, 12:46
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