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If an integer is divisible by both 8 and 15, then the integer also mus

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If an integer is divisible by both 8 and 15, then the integer also mus  [#permalink]

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New post 26 Jun 2018, 20:43
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87% (01:00) correct 13% (01:10) wrong based on 86 sessions

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Re: If an integer is divisible by both 8 and 15, then the integer also mus  [#permalink]

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New post 26 Jun 2018, 21:39
If a number is divisible by 8, and 15 . Its factors are
\(2^3\), 3 and 5. More values could be there but these are min.
Explore the options
A. 16 = \(2^4\) could be or cant be.
B. 24 = \(2^3 * 3\). suffice within the factors Must be
C. 32 = \(2^5\).could be or cant be

D. 36 =\(2^4 * 3^2\)..could be or cant be


E. 45 = \(3^2 * 5\) . could be or cant be
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Re: If an integer is divisible by both 8 and 15, then the integer also mus  [#permalink]

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New post 26 Jun 2018, 21:47

Solution



Given:
    • An integer is divisible by both 8 and 15

To find:
    • From the given options, which integer must divide the given number

Approach and Working:
If a number is divisible by both 8 and 15, then it should also be divisible by the LCM of 8 and 15
    • LCM (8, 15) = 120

Now, if 120 can divide a certain number, any factor of 120 can also divide that number
    • Among the options given, only 24 is a factor of 120

Hence, the correct answer is option B.

Answer: B
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Re: If an integer is divisible by both 8 and 15, then the integer also mus  [#permalink]

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New post 27 Jun 2018, 07:19
Bunuel wrote:
If an integer is divisible by both 8 and 15, then the integer also must be divisible by which of the following?

A. 16

B. 24

C. 32

D. 36

E. 45


Let N be the number which is divisible by \(8(2^3)\) and \(15(3*5)\)

Therefore, Only Option B(\(24 = 2^3*3\)) divides the number N and is our answer.

P.S Prime-factorizing the remaining answer options gives us a higher power of the prime-numbers(in 8 and 15)
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Re: If an integer is divisible by both 8 and 15, then the integer also mus  [#permalink]

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New post 02 Jul 2018, 10:04
Bunuel wrote:
If an integer is divisible by both 8 and 15, then the integer also must be divisible by which of the following?

A. 16

B. 24

C. 32

D. 36

E. 45


Since the LCM of 8 and 15 is 120, the integer is divisible by 120 and by any factors of 120. Since 24 is a factor of 120, the integer is divisible by 24.

Answer: B
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Re: If an integer is divisible by both 8 and 15, then the integer also mus  [#permalink]

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New post 04 Jul 2018, 04:44
Bunuel wrote:
If an integer is divisible by both 8 and 15, then the integer also must be divisible by which of the following?

A. 16

B. 24

C. 32

D. 36

E. 45



The integer must be equal to the LCM of 8 and 15 which is 120.

24*5 = 120 . So, The correct answer is B as it is a factor of 120.
Re: If an integer is divisible by both 8 and 15, then the integer also mus &nbs [#permalink] 04 Jul 2018, 04:44
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