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

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Math Revolution GMAT Instructor
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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24 Jan 2018, 01:36
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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

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7952 Re: What is the least common multiple of 6, 12, 20, 30 and 42? [#permalink] ### Show Tags 24 Jan 2018, 02:15 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 A straight answer.. 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 _________________ Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4751 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: What is the least common multiple of 6, 12, 20, 30 and 42? [#permalink] ### Show Tags 24 Jan 2018, 02:39 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 _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Intern 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] ### Show Tags 24 Jan 2018, 18:46 1 210 cannot be answer chetan, 210 is not divisible by 12 Sent from my SM-G955U using GMAT Club Forum mobile app CEO Joined: 12 Sep 2015 Posts: 3990 Location: Canada Re: What is the least common multiple of 6, 12, 20, 30 and 42? [#permalink] ### Show Tags 24 Jan 2018, 18:52 Top Contributor adityanahan wrote: 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 _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor 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] ### Show Tags 26 Jan 2018, 01:19 => 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. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Target Test Prep Representative
Affiliations: Target Test Prep
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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26 Jan 2018, 10:37
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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Re: What is the least common multiple of 6, 12, 20, 30 and 42?   [#permalink] 26 Jan 2018, 10:37
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