Maths problem (probably a mistake in the book)

[Arkadia]

I am thinking of a number. My number is the first multiple of both 5 and 100. What is my number?

[museumum]

100?

(Though am ropey on terminology at school level)

[viques]

100

[sirfredfredgeorge]

or 0 (0x5, 0x100)
or 1 (0.25 0.01100)

0 or 1 are surely more first than 100?

[MyOtherProfile]

0 or 1 are factors, not multiples, aren't they?

[MyOtherProfile]

Is say 100

[Whynotnowbaby]

Why do you think it’s a mistake? As others said it’s 100.

[Blueemeraldagain]

It’s a badly written question. I think the OP has read it as the first multiple of 5 (5) and the first multiple of 100 (100) not the first possible multiple of 5 and 100 at the same time.

I’m not explaining this well.

[user789653241]

I think it's 100 too. And sir, I don't think 0 or 1 are multiple of 5 or 100.

[BoneyBackJefferson]

500
LCM?

[Arkadia]

Ooohhh.... How stupid of me (well, us if you count DD :D )
"First" as in "first common". I read it as in "first multiple of each number".

[Arkadia]

Exactly bluee :D

[Blueemeraldagain]

Lowest common multiple. That’s the phrase I (and the question) was missing!

[sirfredfredgeorge]

I cannot see any definition of multiple where 0 is not a multiple, so the problem is if 0 is more first than 100...

[ChardonnaysPrettySister]

5

[TheAntiBoop]

Sir - lowest common multiple will mean the lowest number that the two numbers you have can go into. It can not be less than the larger number

[dementedpixie]

100 doesn't go into 5 so out can't be 5

[dementedpixie]

It not out

[ChardonnaysPrettySister]

100 divided by 20 is 5
5 divides by itself

So lowest common denominator is 5.

Unless we are looking for something else?

[catkind]

Lowest common multiple is by definition the smallest positive integer that is a multiple of both numbers. It may be that's what the question was trying to get at, but they forgot to say positive or use the phrase LCM.

I think it's reasonable to assume 1 is not counted as a multiple, we had this conversation before recently and it was an interesting one, but unless specified otherwise you have to assume in school maths that "multiple" means "integer multiple".

However, the definition of multiple of 5 doesn't usually exclude the multiple 0x5=0. Hence it needing specifying extra in the definition of LCM.

Come to that, -100 is also a multiple of 5 and of 100. Does that come first?

[catkind]

Chardonnay, you're thinking of the greatest common divisor. 5 is a divisor of 100, not a multiple of it. 100 = 20 x 5 is a multiple of 5.

[sirfredfredgeorge]

Oh yes, you imagine that lowest common multiple is what's wanted, first multiple is just an odd way of asking for it - of course, in context it may not be, e.g. if the worksheet has "Lowest Common Multiples" at the top.
(I will of course concede it can't be 1 with the likely primary definition of multiple, so everything catkind said.)

[ChardonnaysPrettySister]

Oh ok.

I was a bit surprised with myself for diving into a maths thread anyway.

[user789653241]

I think people are thinking too much if they are thinking something else than LCM on primary board on the said question, imo.