What is the lowest positive integer that is divisible by

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

What is the lowest positive integer that is divisible by

by VJesus12 » Thu Jun 28, 2018 4:56 am

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What is the lowest positive integer that is divisible by each of the even integers between 1 and 10, inclusive?

A. 60
B. 100
C. 120
D. 160
E. 240

The OA is the option C.

How can I find the correct answer here? Could anyone give me a good approach? Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Jun 28, 2018 4:56 am

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Thu Jun 28, 2018 11:31 am

Hi VJesus12,

We're asked for the SMALLEST positive integer that is divisible by each of the EVEN integers between 1 and 10, inclusive. This question can be solved rather easily by TESTing THE ANSWERS. Since we're asked for the SMALLEST number, we should start with Answer A and then work our way 'up' until we find the one that matches...

Answer A: 60.... is 60 divisible by 2, 4, 6, 8 and 10.... NO, it's not divisible by 8.
Answer A: 100.... is 100 divisible by 2, 4, 6, 8 and 10.... NO, it's not divisible by 6 or 8.
Answer A: 120.... is 120 divisible by 2, 4, 6, 8 and 10.... YES, it's divisible by all the values (re: 2x60, 4x30, 6x20, 8x15, 10x12).

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Mon Jul 02, 2018 8:49 am

VJesus12 wrote:What is the lowest positive integer that is divisible by each of the even integers between 1 and 10, inclusive?

A. 60
B. 100
C. 120
D. 160
E. 240

We need to determine the smallest number that is divisible by the following:

2, 4, 6, 8, and 10

That is, we need to find the least common multiple (LCM) of 2, 4, 6, 8, and 10:

In prime factorization form, we have:

2, 2^2, 2 x 3, 2^3, 2 x 5

So the LCM is 2^3 x 3 x 5 = 8 x 15 = 120.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]