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

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New post 24 Jan 2018, 01:36
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E

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Question Stats:

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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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Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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New post 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
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Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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New post 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
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Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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New post 24 Jan 2018, 18:46
1
210 cannot be answer chetan, 210 is not divisible by 12

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Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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New post 24 Jan 2018, 18:52
Top Contributor
adityanahan wrote:
210 cannot be answer chetan, 210 is not divisible by 12

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??
210 is not among the answer choices :-)
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Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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New post 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
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Re: What is the least common multiple of 6, 12, 20, 30 and 42?  [#permalink]

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New post 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

Answer: E
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Re: What is the least common multiple of 6, 12, 20, 30 and 42? &nbs [#permalink] 26 Jan 2018, 10:37
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