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

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Math Expert
Joined: 02 Sep 2009
Posts: 50007
What is the least common multiple of 18,120, 216, and 1080?  [#permalink]

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31 Dec 2017, 14:23
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Difficulty:

25% (medium)

Question Stats:

80% (02:17) correct 20% (03:02) wrong based on 80 sessions

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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

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Posts: 721
Re: What is the least common multiple of 18,120, 216, and 1080?  [#permalink]

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31 Dec 2017, 14:41
1
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!
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Re: What is the least common multiple of 18,120, 216, and 1080?  [#permalink]

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15 Feb 2018, 19:27
Is there a quicker way than factoring all of them? Should I have known that those were all factors of 1080?

Maybe I just need to speed up my factoring, but this one took me a touch over 3 minutes.
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Posts: 1838
Re: What is the least common multiple of 18,120, 216, and 1080?  [#permalink]

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15 Feb 2018, 21:14
jsheppa wrote:
Is there a quicker way than factoring all of them? Should I have known that those were all factors of 1080?

Maybe I just need to speed up my factoring, but this one took me a touch over 3 minutes.

Hi,

If you look carefully to the question, you might find a key or pattern.

1- Look to the above solution, when see number X ends with 0, then make two multiplied numbers, x = 'A * 10'

2- Let's see 1080 = 108 * 10. If you tried to factor 108 I started to divide b 3 so I got 108 = 3 * 36.....So I quickly recognized it is 3 * 6^2. and you can continue.

I detailed process above. However, You need to practice to and hence you will get the skill.
Re: What is the least common multiple of 18,120, 216, and 1080? &nbs [#permalink] 15 Feb 2018, 21:14
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