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

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

by Max@Math Revolution » Wed Jan 24, 2018 12:21 am
[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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by GMATGuruNY » Wed Jan 24, 2018 3:32 am
Max@Math Revolution 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
To be a multiple of 42, the correct answer must be divisible by 7.
Of the five answer choices, only 420 is divisible by 7.

The correct answer is E.
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by Max@Math Revolution » Fri Jan 26, 2018 12:11 am
=>

These numbers have the following prime factorizations:
$$6=2^1\cdot3^1,\ 12=2^2\cdot3^1,\ 20=2^2\cdot5^1,\ 30=2^1\cdot3^1\cdot5^1\ and\ \ 42=2^1\cdot3^1\cdot7^1$$

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 $$2^2\cdot3^1\cdot5^1\cdot7^1=420$$
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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by Jeff@TargetTestPrep » Fri Jan 26, 2018 9:51 am
Max@Math Revolution 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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