Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 06:44 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which of the following is the lowest positive integer that is

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56251
Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 68% (01:41) correct 32% (02:07) wrong based on 260 sessions

### HideShow timer Statistics Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?

A. 15,120
B. 3,024
C. 2,520
D. 1,890
E. 1,680

_________________
Director  V
Joined: 04 Dec 2015
Posts: 745
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

2
2
Bunuel wrote:
Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?

A. 15,120
B. 3,024
C. 2,520
D. 1,890
E. 1,680

Lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9 would be LCM of 2, 3, 4, 5, 6, 7, 8, and 9.

Prime factorization of 2, 3, 4, 5, 6, 7, 8, and 9.

$$2 = 2$$
$$3 = 3$$
$$4 = 2* 2 = 2^2$$
$$5 = 5$$
$$6 = 2 * 3$$
$$7 = 7$$
$$8 = 2*2*2 = 2^3$$
$$9 = 3 * 3 = 3^2$$

LCM of 2, 3, 4, 5, 6, 7, 8, and 9 $$= 2^3 * 3^2 * 5 * 7 = 2520.$$ Answer (C)...
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3360
Location: India
GPA: 3.12
Re: Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

In other words, the question asks us to identify the LCM of the numbers 2,3,4,5,6,7,8 and 9

The numbers, when prime factorized and on identifying the highest power of each prime number,
we get the following number : 5 * 7 * 8(2^3) * 9(3^2) = 35 * 72 = 2520(Option C)
_________________
You've got what it takes, but it will take everything you've got
Senior Manager  B
Joined: 28 Jun 2015
Posts: 286
Concentration: Finance
GPA: 3.5
Re: Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

Bunuel wrote:
Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?

A. 15,120
B. 3,024
C. 2,520
D. 1,890
E. 1,680

Option (E) can be ignored as it is not divisible by 9.

Next lowest number is 1890, which is not divisible by 4 or 8.

Option (C) is divisible by 3,6,7,8,9. Hence Ans - C.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Intern  B
Joined: 28 Apr 2017
Posts: 1
Re: Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

It must be devisible by both 2 and 5 so by 10.
The last two digit must be devided by 4
Finally the sum of all digits must be devided by 9
OA is C

Sent from my Nexus 5 using GMAT Club Forum mobile app
Current Student S
Joined: 06 Nov 2016
Posts: 103
Location: India
GMAT 1: 710 Q50 V36 GPA: 2.8
Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

LCM of these numbers: 2,520 answer
IMO C
Current Student B
Joined: 16 May 2017
Posts: 11
Location: United States
GMAT 1: 630 Q40 V36 GMAT 2: 760 Q50 V42 GPA: 3.55
Re: Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

To be divisible by all of those numbers, it must have all of the prime factors of each of those numbers.

Break down of prime factors
2 - 2
3 - 3
4 - 2 x 2
5 - 5
6 - 2 x 3
7 - 7
8 - 2 x 2 x 2
9 - 3 x 3

The number must have all the qualifying factors for each of those numbers so:
2^3 x 3^2 x 5 x 7 = 2520
Director  D
Joined: 13 Mar 2017
Posts: 731
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

Bunuel wrote:
Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?

A. 15,120
B. 3,024
C. 2,520
D. 1,890
E. 1,680

Since we have to check the numbers for the divisibility by 2, 3, 4, 5, 6, 7, 8, 9 ... We just need to check the divisibility by 5,7,8,9

So we will start checking the options one by one for the divisibility by 5,7,8, 9.

To solve the problem in a faster way, we need to go through options very smartly and hence recheck the question. (I solved the question in 2:40 seconds which is on the higher side because I checked the divisibility of each number by 5,7,8,9 and there were 2 numbers divisible by all then I noticed that the question is asking for lowest positive integer.)

So how to solve this problem in smartly and in timely manner.

what to keep in mind.
1. As the question says we need to find the lowest positive integer divisible. So we should start from the lowest integer in the options.
2. We need to start from the number for which divisibility check is easier e.g. 5

Shortest way : Since this question ask for the lowest positive integer divisible by numbers .
This is the LCM of numbers 5x7x8x9 = 2520 Answer C.

Shorter way : If the question would have asked for lowest positive integer from the options.
Then,
1st check 1680 : Divisible by 5, Divisible by 8 , But not divisible by 9. No need to check divisibility by 7.
2nd 1890 : Divisible by 5, Not divisible by 8. No need to check divisibility by 9 and 7
3rd 2520 : Divisible by 5, divisible by 8, divisible by 9 , divisible by 7

So C is the correct option.

Finally don't forget to give kudos.. _________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

1
Bunuel wrote:
Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?

A. 15,120
B. 3,024
C. 2,520
D. 1,890
E. 1,680

We need to determine the least common multiple (LCM) of 2, 3, 4, 5, 6, 7, 8, and 9. Breaking each of these into primes, we have:

2^1, 3^1, 2^2, 5^1, 2^1 x 3^1, 7^1, 2^3, 3^2

To find the LCM, we need to use each prime number from the above list and we need that prime number as many times as its highest exponent. Let’s first consider 2. Look at all of the occurrences of the prime number 2 from the previous list: 2^1, 2^2, 2^1, 2^3. Since the highest power of 2 is 3, we will use 2^3 as one of the factors in the LCM. Similarly, the prime number 3 occurred in the list as 3^1, 3^1, and 3^2. Thus, we will use 3^2 as one of the factors in the LCM. Note that 5 occurred only as 5^1 and that 7 occurred only as 7^1; thus, the numbers 5^1 and 7^1 will be the final two factors of the LCM.

Thus, the LCM is 2^3 x 3^2 x 5 x 7 = 8 x 9 x 5 x 7 = 2,520.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 11694
Re: Which of the following is the lowest positive integer that is  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Which of the following is the lowest positive integer that is   [#permalink] 26 Sep 2018, 14:16
Display posts from previous: Sort by

# Which of the following is the lowest positive integer that is  