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What is the least common multiple of 18,120, 216, and 1080?

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Expert Post
Math Expert
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V
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139605 [0], given: 12794

What is the least common multiple of 18,120, 216, and 1080? [#permalink]

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New post 31 Dec 2017, 13:23
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

82% (01:17) correct 18% (03:46) wrong based on 22 sessions

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Kudos [?]: 139605 [0], given: 12794

Expert Post
examPAL Representative
User avatar
B
Joined: 07 Dec 2017
Posts: 117

Kudos [?]: 21 [0], given: 3

Re: What is the least common multiple of 18,120, 216, and 1080? [#permalink]

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New post 31 Dec 2017, 13:41
Bunuel wrote:
What is the least common multiple of 18,120, 216, and 1080?

A. 1,080
B. 19,440
C. 38,680
D. 38,860
E. 38,880


To answer a question involving least common multiples it is usually helpful to look at prime factorizations.
This is a Precise approach.

18 factors into 3*3*2
120 factors into 12*10 = 2*2*3*5*2
216 factors into 2*108 = 2*3*36 = 2*3*4*9 = (2*2*2)*(3*3*3)
1080 factors into 10*108 = 10*(2*2*2)*(3*3*3)=(2*2*2*2)*(3*3*3)*5

The least common multiple involves the prime factors of all of the above.
Therefore, we need to count the largest number of 2's, 3's and 5's in the above numbers.
1080 has four 2's, 216 and 1080 have three 3's and 120, 1080 have one 5.
Therefore the least common multiple has four 2's, three 3's and one 5.
These are exactly the factors of 1080!
Therefore our answer is (A)
_________________

David
Senior tutor at examPAL
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Kudos [?]: 21 [0], given: 3

Re: What is the least common multiple of 18,120, 216, and 1080?   [#permalink] 31 Dec 2017, 13:41
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What is the least common multiple of 18,120, 216, and 1080?

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