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What is the greatest positive three-digit number that is div

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by Max@Math Revolution » Wed Feb 20, 2019 11:55 pm

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[GMAT math practice question]

What is the greatest positive three-digit number that is divisible by 2, 3, 4, 5, 6 and 7?

A. 120
B. 140
C. 210
D. 420
E. 840
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by Brent@GMATPrepNow » Thu Feb 21, 2019 11:40 am
Max@Math Revolution wrote:[GMAT math practice question]

What is the greatest positive three-digit number that is divisible by 2, 3, 4, 5, 6 and 7?

A. 120
B. 140
C. 210
D. 420
E. 840
One approach is to check each answer choice, beginning with the largest answer choice

E. 840
840 is divisible by 2, 3, 4, 5, 6 and 7
Answer: E

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by Scott@TargetTestPrep » Sun Feb 24, 2019 5:29 am
Max@Math Revolution wrote:[GMAT math practice question]

What is the greatest positive three-digit number that is divisible by 2, 3, 4, 5, 6 and 7?

A. 120
B. 140
C. 210
D. 420
E. 840
The LCM of 2, 3, 4, 5, 6, and 7 is:

3 x 4 x 5 x 7 = 420, so the greatest positive three-digit number that is divisible by 2, 3, 4, 5, 6, and 7 is 420 x 2 = 840.

Answer: E

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by Max@Math Revolution » Sun Feb 24, 2019 5:37 am
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The question asks for the value of the greatest positive three-digit multiple of lcm(2,3,4,5,6,7), where lcm(2,3,4,5,6,7) is the least common multiple of 2, 3, 4, 5, 6 and 7.
lcm(2,3,4,5,6,7) = 2^2*3*5*7 = 420.
There are two positive three-digit integers that are multiples of 420: 420 and 840.
The greatest positive three-digit number that is a multiple of 420 is 840.

Therefore, the answer is E.
Answer: E
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