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What is the least common multiple of 39, 91, 93 and 217?

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by Max@Math Revolution » Mon Feb 12, 2018 1:07 am
[GMAT math practice question]

What is the least common multiple of 39, 91, 93 and 217?

A. 8461
B. 8462
C. 8463
D. 8464
E. 8465
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What is the least common multiple of 39, 91, 93 and 217?

by EconomistGMATTutor » Tue Feb 13, 2018 1:27 pm
GMAT math practice question]

What is the least common multiple of 39, 91, 93 and 217?

A. 8461
B. 8462
C. 8463
D. 8464
E. 8465
Hi Max@Math Revolution,
Let's take a look at your question.

To find the least common multiples of given numbers, we need to write the numbers a product of their prime factors.

39 = 3 x 13
91 = 7 x 13
93 = 3 x 31
217 = 7 x 31

Common Factors = 3, 13, 7, 31
Least Common Multiple = 3 x 13 x 7 x 31 = 8463

Therefore, Option C is correct.

Hope it helps. I am available if you'd like any follow up.
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by Scott@TargetTestPrep » Tue Feb 13, 2018 5:32 pm
Max@Math Revolution wrote:[GMAT math practice question]

What is the least common multiple of 39, 91, 93 and 217?

A. 8461
B. 8462
C. 8463
D. 8464
E. 8465
Prime factorizing each number, we have:

39 = 13 x 3

91 = 13 x 7

93 = 3 x 31

217 = 31 x 7

So the LCM is:

13 x 3 x 31 x 7

Rather than multiplying out the values, we can just calculate the units digit of our product by multiplying:

3 x 3 x 1 x 7 = 63, so the correct answer ends in a 3.

Answer: C

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by Max@Math Revolution » Tue Feb 13, 2018 11:57 pm
=>

Since 39 = 3 * 13, the least common multiple must be a multiple of 3.
The sum of the digits of a multiple of 3 is a multiple of 3.
8643 is the only answer choice for which the sum of the digits is a multiple of 3: 8 + 4 + 6 + 3 = 21 = 3 * 7.

Therefore, C is the answer.

Alternatively, since 39 = 3*13, 91 = 7*13, 93 = 3*31, and 217=7*31, the least common multiple of the four numbers is 3*7*13*31 = 8463.

Therefore, the answer is C.

Answer: C
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