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What is the least common multiple of 39, 91, 93 and 217? 12 Feb 2018, 02:12
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C
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[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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C
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What is the least common multiple of 39, 91, 93 and 217? 12 Feb 2018, 02:26
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MathRevolution
[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 the numbers,
39 = 3*13
91 = 7*13
93 = 3*31
217 = 7*31

The LCM is 3*7*13*31 whose unit digit is 3 and the answer option ending 3 is 8463(Option C)
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What is the least common multiple of 39, 91, 93 and 217? 12 Feb 2018, 02:30
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Factor of 39 =3*13
............ 91= 7*13
............ 93= 3*31
............ 217= 7*31

Least Common Multiple is the highest power of all the factors: 3*7*13*31= 8463

Answer: C.
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What is the least common multiple of 39, 91, 93 and 217? 12 Feb 2018, 03:06
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MathRevolution
[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..
You don't have to do actuals calculation..
1) 39 and 93 are multiple of 3, so our LCM should be MULTIPLE of 3..
8463=8+4+6+3=21, hence a MULTIPLE of 3..
Others are 1 or 2 more or less than it.. so none other is MULTIPLE of 3..
Ans C
2) there is no even number, so B and D are out
3) there is no 5, so E is out..


C
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What is the least common multiple of 39, 91, 93 and 217? 13 Feb 2018, 17:58
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MathRevolution
[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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What is the least common multiple of 39, 91, 93 and 217? 14 Feb 2018, 01:22
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=>

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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What is the least common multiple of 39, 91, 93 and 217? 29 Mar 2022, 13:02
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