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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
What is the greatest positive three-digit number that is divisible by  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 65% (01:04) correct 35% (00:52) wrong based on 37 sessions

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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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Concentration: Accounting, Finance
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What is the greatest positive three-digit number that is divisible by  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

$$A. 120$$
$$B. 140$$
$$C. 210$$
$$D. 420$$
$$E. 840$$

Option E) 840.

last digit is 0. thus, it's divisible by 2 and 5.

8 + 4 + 0 = 12 . Thus it's divisible by 3.

A number that is divisible by both 2 and 3 is also divisible by 6.

last 2 digit is divisible by 4 thus, 840 is divisible by 4.

7*12 = 84.

So, 840 is the greatest integer that meets the condition.

The best answer is E.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the greatest positive three-digit number that is divisible by  [#permalink]

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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.
_________________ Re: What is the greatest positive three-digit number that is divisible by   [#permalink] 24 Feb 2019, 06:59
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