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# What is the greatest positive three-digit number that is divisible by

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7107
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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21 Feb 2019, 01:21
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Difficulty:

25% (medium)

Question Stats:

65% (01:13) correct 35% (01:00) wrong based on 23 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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Joined: 31 Oct 2013 Posts: 1273 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) What is the greatest positive three-digit number that is divisible by [#permalink] ### Show Tags 21 Feb 2019, 01:27 1 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 Joined: 16 Aug 2015 Posts: 7107 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the greatest positive three-digit number that is divisible by [#permalink] ### Show Tags 24 Feb 2019, 06:59 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: What is the greatest positive three-digit number that is divisible by   [#permalink] 24 Feb 2019, 06:59
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