The least common multiple of positive integer m and 3-digit

Question

The least common multiple of positive integer m and 3-digit integer n is 690. If n is not divisible by 3 and m is not divisible by 2, what is the value of n?

A. 115
B. 230
C. 460
D. 575
E. 690

mau5 · Accepted Answer

I will throw in my approach, I am sure Bunuel will have a better method

Prime Factorisation of 690 = 2*3*5*23

Now, n is not divisible by 3. Thus, as \frac{690}{n} = Integer, n can be : 2*5*23 or 5*23

Again, as  \frac{690}{m}  = Integer, and also, as m is not divisible by 2, m can be : 3*5*23 or 3 or 5 or 3*5 or 5*23 or 3*23 or 23.

However, as a single 2 is present in 690's prime factorisation, and as m is not divisible by 2, the only way we can get it is when n = 2*5*23.

Thus n = 230

B.

Bunuel · Answer

The LCM of n and m is 690 = 2*3*5*23.

m is not divisible by 2, thus 2 goes to n
n is not divisible by 3, thus 3 goes to m.

From above:
n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.

Answer: B.

honchos · Answer

The question is not tough rather tricky, more about how much one understand LCM concept. I did it wrong I opted for 115, which is a wrong answer.

Its solution from Bunuel will be much appreciated.

Thanks!

PareshGmat · Answer

Did not do any calculations here; just look at the options

LCM = 690 & n is 3 digit>> it implies that  m is a single digit number

n CANNOT be greater than 345 (690/2) as m is single digit

So options C, D, E can be discarded

If n is not divisible by 3 and m is not divisible by 2

This means that m is divisible by 3 & n is divisible by 2

From the options, 230 best fits in.

Answer = B

samirchaudhary · Answer

I used elimination :

'n' is not divisible by 3 => We can eliminate option 'e'.

'm' is not divisible by 2 => 'n' has to be a multiple of 2. => Eliminate 'a' and 'd' which are odd integers.

We are left with '230' and '460'.

We can eliminate '460' caz '690' is not a multiple of '460'.

So the correct answer is '230'.

TeamGMATIFY · Answer

Given  : LCM of positive integer m and 3-digit integer n is 690. n is not divisible by 3 and m is not divisible by 2
  Required  : n =?

690 = 23*5*3*2
Since 690 is the LCM of m and n. Hence at-least on of n or m should have these values in their factors.

m is not divisible by 2. This means n is divisible by 2.
Options left B, C, E

n is not divisible by 3
Options left B and C

Since n has to be a three digit number not divisible by 3, it will need to have all the other numbers out of 23, 5 and 2 (We cannot give 2 to m and n cannot take 3)
Hence n = 230
Option B

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The least common multiple of positive integer m and 3-digit

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