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If j is a multiple of 12, and k is a multiple of 21, then jk must be a

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Bunuel
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If j is a multiple of 12, and k is a multiple of 21, then jk must be a [#permalink] New post   31 Oct 2018, 00:56
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If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

A. 8
B. 15
C. 22
D. 28
E. 35
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D
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Re: If j is a multiple of 12, and k is a multiple of 21, then jk must be a [#permalink] New post   31 Oct 2018, 01:13
Bunuel wrote:
If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

A. 8
B. 15
C. 22
D. 28
E. 35



j = 12k

k = 21k

Lcm of 12 and 21 : 84 ...........the minimum value of jk

Option 28 is the answer.

28 * 3 = 84.
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Re: If j is a multiple of 12, and k is a multiple of 21, then jk must be a [#permalink] New post   31 Oct 2018, 02:29
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Bunuel wrote:
If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

A. 8
B. 15
C. 22
D. 28
E. 35


j = 12a
k = 21b

\(jk = 12*21 * a * b = 2^2 * 3^2 * 7 * ab\)

The option which is a factor of 2^2 * 3^2 * 7 will be correct.
\(28 = 2^2 * 7\)

Answer (D)
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Re: If j is a multiple of 12, and k is a multiple of 21, then jk must be a [#permalink] New post   01 Jul 2020, 07:29
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Bunuel wrote:
If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

A. 8
B. 15
C. 22
D. 28
E. 35


j is a multiple of 12
This means we can write j = 12n (for some integer n)

k is a multiple of 21
This means we can write k = 21m (for some integer m)

jk must be a multiple of which of the following?
jk = (12n)(21m)
= (4)(3)(n)(7)(3)(m)
= (28)(3)(n)(3)(m)

Clearly, jk is a multiple of 28

Answer: D
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Re: If j is a multiple of 12, and k is a multiple of 21, then jk must be a [#permalink] New post   10 Jul 2020, 04:51
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Bunuel wrote:
If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

A. 8
B. 15
C. 22
D. 28
E. 35


Solution:

Since j is a multiple of 12 and k is a multiple of 21, jk must be a multiple of the LCM of 12 and 21 and all its factors. Since the LCM of 12 and 21 is 3 x 4 x 7 = 84 and one of its factors is 28, jk is a multiple of 28.

Answer: D
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Re: If j is a multiple of 12, and k is a multiple of 21, then jk must be a [#permalink] New post   09 Jan 2024, 11:00
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Re: If j is a multiple of 12, and k is a multiple of 21, then jk must be a [#permalink]
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