[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
What is the greatest positive three-digit number that is div
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- Max@Math Revolution
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One approach is to check each answer choice, beginning with the largest answer choiceMax@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
E. 840
840 is divisible by 2, 3, 4, 5, 6 and 7
Answer: E
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The LCM of 2, 3, 4, 5, 6, and 7 is: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
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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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
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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