# common multiple

#### sufinaz

##### New member
I think of two different numbers between 100 and 200 inclusive, highest common factor is the same as the lowest common multiple of 8 and 10. what two numbers could I have thought of?

#### MarkFL

##### Super Moderator
Staff member
Well, what is the lcm of 8 and 10?

2 ?

#### Subhotosh Khan

##### Super Moderator
Staff member
I think of two different numbers between 100 and 200 inclusive, highest common factor is the same as the lowest common multiple of 8 and 10. what two numbers could I have thought of?
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#### Subhotosh Khan

##### Super Moderator
Staff member
No ..... Please review the method of calculating LCM and GCF - before trying to go further!

#### MarkFL

##### Super Moderator
Staff member
No, 2 is neither a multiple of 8 or 10. There is a way to obtain the lcm of two numbers based on their prime factorization, but I would simply suggest you list the first several multiples of both numbers (8 and 10) until you find one that is common to both.

#### Subhotosh Khan

##### Super Moderator
Staff member
Multiple of a number will be bigger than (or equal to the) number.

So LCM of 8 and 10 will be bigger than 10.

#### firemath

##### Full Member
2 is a factor, not a multiple. Factors are the multiplicative "makeup" of a number, and a multiples are what you get when you multiply two values.

#### pka

##### Elite Member
I think of two different numbers between 100 and 200 inclusive, highest common factor is the same as the lowest common multiple of 8 and 10. what two numbers could I have thought of?
When one need to say "between 100 and 200 inclusive " it is stand to use 'from 100 to 200'.
If it is not inclusive then it is "between 100 & 200".
Both numbers must be a multiple of $$\displaystyle 40=2^3\cdot 5$$. But both must exceed $$\displaystyle 100$$ while $$\displaystyle \le 200$$

#### sufinaz

##### New member
so it should be 40
8x5=40
10x4=40

#### firemath

##### Full Member
Beautiful! That's correct.

#### sufinaz

##### New member
still didn't get the question?

#### firemath

##### Full Member
Well, use forty in your inclusive equation.

#### MarkFL

##### Super Moderator
Staff member
still didn't get the question?
Okay, you have correctly determined the lcm of 8 and 10, and so the two numbers must be multiples of 40.

Can you proceed?

#### pka

##### Elite Member
still didn't get the question?
The multiples of $$\displaystyle 40$$ are $$\displaystyle 40,80,120,160,200,240\cdots$$

#### sufinaz

##### New member
between 100 and 200,
there are only 120 an 160 multiple of 40?

#### MarkFL

##### Super Moderator
Staff member
between 100 and 200,
there are only 120 an 160 multiple of 40?
Yes, if the two numbers must be between 100 and 200, then 120 and 160 are the only two such choices.

Staff member

#### pka

##### Elite Member
What happened to 200?
Mr. Khan, 200 is not between 100 & 200.
If we want 100 & 200 included we write "From 100 to 200" or the closed interval 100 to 200.

#### Subhotosh Khan

##### Super Moderator
Staff member
Mr. Khan, 200 is not between 100 & 200.
If we want 100 & 200 included we write "From 100 to 200" or the closed interval 100 to 200.
I know - but the OP specifically stated "inclusive"