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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42 GPA: 3.82
What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 89% (01:30) correct 11% (00:43) wrong based on 59 sessions

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[GMAT math practice question]

What is the least common multiple of 6, 12, 20, 30 and 42?

A. 120
B. 180
C. 240
D. 360
E. 420

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Math Expert V
Joined: 02 Aug 2009
Posts: 7952
Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

What is the least common multiple of 6, 12, 20, 30 and 42?

A. 120
B. 180
C. 240
D. 360
E. 420

42 is the biggest number amongst all 5 numbers and the answer has to be a MULTIPLE of 42 and should have a 0 in the units digit..
Answer canbe 42*5=210(not given) and next 42*10=420..given
E

Otherwise proper method
6=2*3...
$$12=2^2*3$$..
$$20=2^2*5$$..
$$30=2*3*5$$..
$$42=2*3*7$$..
Take max power of each PRIME factor.
LCM=$$2^2*3*5*7=420$$
E
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Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

What is the least common multiple of 6, 12, 20, 30 and 42?

A. 120
B. 180
C. 240
D. 360
E. 420

Check the options provided is straight (E) as reached by chetan2u
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Intern  B
Joined: 03 Nov 2017
Posts: 12
GMAT 1: 590 Q48 V23 Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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1
210 cannot be answer chetan, 210 is not divisible by 12

Sent from my SM-G955U using GMAT Club Forum mobile app
CEO  V
Joined: 12 Sep 2015
Posts: 3990
Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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Top Contributor
210 cannot be answer chetan, 210 is not divisible by 12

Sent from my SM-G955U using GMAT Club Forum mobile app

??
210 is not among the answer choices _________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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=>

These numbers have the following prime factorizations:
$$6 = 2^1*3^1, 12 = 2^2*3^1, 20 = 2^2*5^1, 30 = 2^1*3^1*5^1$$ and $$42 = 2^13^17^1$$

In order to find their LCM, we multiply together each of the primes, raised to their maximum exponents found in the above prime factorizations.
The LCM of the numbers is $$2^2*3^1*5^1*7^1 = 420$$ since the maximum exponent of $$2$$ is $$2$$, the maximum exponent of $$3$$ is $$1$$, the maximum exponent of $$5$$ is $$1$$ and the maximum exponent of $$7$$ is $$1$$.

Therefore, the answer is E.

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Target Test Prep Representative G
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Joined: 04 Mar 2011
Posts: 2817
Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

What is the least common multiple of 6, 12, 20, 30 and 42?

A. 120
B. 180
C. 240
D. 360
E. 420

Let’s prime factorize each value:

6 = 2 x 3

12 = 2^2 x 3

20 = 2^2 x 5

30 = 2 x 3 x 5

42 = 2 x 3 x 7

Multiplying together each unique prime factor (raised to the largest power), we have:

2^2 x 3 x 5 x 7 = 420

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: What is the least common multiple of 6, 12, 20, 30 and 42?   [#permalink] 26 Jan 2018, 10:37
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