- Thread starter sufinaz
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Please follow the rules of posting in this forum, as enunciated at: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 share your

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No ..... Please review the method of calculating LCM and GCF - before trying to go further!

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Multiple of a number will be bigger than (or equal to the) number.

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

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When one need to say "between 100 and 200 inclusive " it is stand to use '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?

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 \(\displaystyle \le 200\)

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

Can you proceed?

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Did you read reply #9?still didn't get the question?

The multiples of \(\displaystyle 40\) are \(\displaystyle 40,80,120,160,200,240\cdots\)

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Yes, if the two numbers must be between 100 and 200, then 120 and 160 are the only two such choices.between 100 and 200,

there are only 120 an 160 multiple of 40?

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between 100 and 200,

there are only 120 an 160 multiple of 40?

What happened to 200?between 100 and 200 inclusive

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Mr. Khan, 200 is not between 100 & 200.What happened to 200?

If we want 100 & 200 included we write "From 100 to 200" or the closed interval 100 to 200.

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I know - but the OP specifically statedMr. 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.

Your response #9 said:

But both must exceed 100 while

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