[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
What is the least common multiple of 39, 91, 93 and 217?
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- Max@Math Revolution
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Hi Max@Math Revolution,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
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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Prime factorizing each number, we have: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
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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- Max@Math Revolution
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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
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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