common multiple

sufinaz

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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

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Well, what is the lcm of 8 and 10?
 

sufinaz

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2 ?
 

Subhotosh Khan

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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?
Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this assignment
 

MarkFL

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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

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firemath

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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

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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

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so it should be 40
8x5=40
10x4=40
 

firemath

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Beautiful! That's correct.
 

sufinaz

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still didn't get the question?
 

firemath

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Well, use forty in your inclusive equation.
 

MarkFL

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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

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still didn't get the question?
Did you read reply #9?
The multiples of \(\displaystyle 40\) are \(\displaystyle 40,80,120,160,200,240\cdots\)
 

sufinaz

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

MarkFL

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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.
 

pka

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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

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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"

Your response #9 said:

But both must exceed 100 while 200

You did put the = sign there .......
 
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