If N is the least positive integer that is a multiple of

Question

If N is the least positive integer that is a multiple of each of the numbers 15, 18, 40, and 50, which of the following statements about N is true?

A. N <= 200 
B. 200 < N <= 2,000 
C. 2,000 < N <= 20,000 
D. 20,000 < N <= 200,000 
E. N> 200,000

Bunuel · Answer

Given that N is the least common multiple of 15, 18, 40, and 50.

15 = 3*5;
18 = 2* 3^2 ;
40 =  2^3 *5;
50 = 2* 5^2 .

N = 2^3*3^2*5^2 = 1,800.

Answer: B.

AccipiterQ · Answer

Is that from some formula for LCM of a group of numbers? I'm curious as to why the 3*5 got ignored when figuring out the answer.

edit: nevermind, google is my friend.

rumimilano · Answer

Well for the sake of the forum, and myself, could you post why exactly 3&5 were ignored?

Posted from my mobile device

AccipiterQ · Answer

To find the lowest common factor of a group of numbers, take the prime factorization of those numbers. For each prime number listed, take the most repeated occurrence of this number in any prime factorization. Then multiply them together.

15 = 3*5;
18 = 2* 3^2;  3 occurs twice in 18 (3^2), it only appears one in 15. 
40 =  2^3 *5; 2 occurs thrice in 40, it only appears once in 18, and once in 50
50 = 2* 5^2 ; 5 occurs twice in 50, it only appears once in 15.

So now that we see the highest power of each prime number that appears in these factorials we multiply them all together:

N = 2^3*3^2*5^2 = 1,800.

TAL010 · Answer

Least Common Multiple = the smallest multiple of two or more integers. The LCM is the lowest product for all of the shared primes. We ignore the 3 and 5 because we are looking to find the lowest common multiple. LCM is not to be confused with the Greatest Common Factor - which is the common factor of ALL integers. They are easily mixed up! :wink:

Now to the problem: Step 1. List the primes for each number 15 - 5,3 18 - 3,3,2 40 - 5,2,2,2 50 - 5,5,2 Step 2. Group common multiples - those that occur the most frequent 5,5(all but 18 have at least one 5 and you must be able to solve for each number given the primes. By having two 5's, we can still solve for 50) 3,3(18 and 15 both have 3, so we need two) 2,2,2 - we need at least three 2's to account for 40. Anything else would be redundant. Step 3:Multiply together (2^3)(5^2)(3^2) = 1800 B is the only option that fits within the perimeters.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If N is the least positive integer that is a multiple of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If N is the least positive integer that is a multiple of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards