Question: Least Common Multiple is 168

Comment on Least Common Multiple is 168

Mr Hanneson. is there any

Mr Hanneson. is there any kind of trick to find the two Integers of a given GCD or LCM other then assumption. if there is can you please direct me towards it.
thank you.

Hi Abdul,

Hi Abdul,

Good question.

First review the following lessons:
Finding the GCD: https://www.greenlighttestprep.com/module/gre-integer-properties/video/832
Finding the LCM: https://www.greenlighttestprep.com/module/gre-integer-properties/video/834

Those videos will give you an idea of how to come up with values that satisfy certain conditions. That said, here are some quick pointers:

GREATEST COMMON DIVISOR (GCD)
If we know that the GCD of two numbers is k, then the two numbers can be k and any multiple of k
So, if the GCD of two numbers is 11, then the two numbers can be 11 & 22, or 11 & 55 OR 11 & 11, etc.
There are other strategies we can apply, but the above approach works in a pinch.

LEAST COMMON MULTIPLE (LCM)
If we know that the LCM of two numbers is q, then the two numbers can be q and any divisor of q
So, if the LCM of two numbers is 18, then the two numbers can be 18 & 6, or 18 & 1 OR 18 & 9, or 18 & 18, etc.

Cheers,
Brent

I have to say Mr Hanneson,

I have to say Mr Hanneson, your program is a life saver. It has indeed been a tremendous help to me. Your Lecture series are the most comprehensible and lucid lectures I have ever encountered.

Thank you very much

Cheers,
Abdul Hannan.

Thanks Abdul! That's nice of

Thanks Abdul! That's nice of you to say.

Cheers,
Brent

HI Brent,

HI Brent,
plz can you help me out with in understanding the question.

1. https://gre.myprepclub.com/forum/the-number-of-multiples-of-3-between-102-and-729-inclusive-8843.html

2. How many multiples of 5 are there between 81 and 358

3. How many multiples of 7 are there between 21 and 343, exclusive .

I am really confused with the wordings inclusive , between and exclusive.

However I derived from the following equation Multiples of 5 = {(Last multiple -First multiple)/5} +1

but the inclusive , between and exclusive does all mean the same?

INCLUSIVE means we INCLUDE the numbers on either side of the list of values.
So, the integers from 3 to 8 INCLUSIVE are: 3, 4, 5, 6, 7, and 8

Aside: It's grammatically incorrect to use BETWEEN and INCLUSIVE (e.g., the integers BETWEEN 3 and 8 INCLUSIVE).
The generally used form is: "The integers FROM 3 to 8 INCLUSIVE"

EXCLUSIVE means BETWEEN (in fact, most GRE resources will use BETWEEN). In other words, we DON'T INCLUDE the numbers on either side of the list of values.
So, the integers BETWEEN 3 and 8 are: 4, 5, 6, and 7

In general, use the formula for INCLUSIVE.
That is: Multiples of k = (Last multiple of k - First multiple of k)/k} +1

We get:
1. The number of multiples of 3 between 102 and 729, inclusive
First multiple = 3. Last multiple = 729
Number of multiples of 3 = (729 - 102)/3 + 1

2. How many multiples of 5 are there BETWEEN 81 and 358?
First multiple = 85. Last multiple = 355
Number of multiples of 5 = (355 - 85)/5 + 1

3. How many multiples of 7 are there between 21 and 343, EXCLUSIVE?
This is the same as "How many multiples of 7 are there BETWEEN 21 and 343?"
First multiple = 28. Last multiple = 336
Number of multiples of 7 = (336 - 28)/7 + 1

Cheers,
Brent

Thanks Brent,

Thanks Brent,

In any case we have to follow : Multiples of k = (Last multiple of k - First multiple of k)/k} +1

Only difference, choosing numbers in the given set, whether the first and the last term are included or excluded

That's correct.

Thanks Brent

Hi Brent,

Hi Brent,

If there are 3 number, how to apply to use this formular?

As far as I know, there isn't

As far as I know, there isn't a convenient formula for 3 values.
More importantly, the GRE won't test you on this.

Cheers,
Brent

I am trying to think of some

I am trying to think of some way to solve it without the formula, but can't find any logic. It is more because of curiosity. Can you help me with it, please?

As I mentioned in the

As I mentioned in the previous comment. I think that I found some way to do it, but it is kind of a trying way. Will be nice to hear your opinion.
From the GCD part:
G = 24a
H = 24b
From the LCM part:
168/(24a) = b
a*b = 7

Now we have enough information to solve the problem.
G*H = 24a * 24b
G*H = 24*24*ab
We know that ab = 7
So,
GH = 24*24*7

GH/48 = (24*24*7)/48 = 84

Beautiful solution!

Beautiful solution!