Is 0 a multiple of every number?

[PrashantS209]

I got this question in GMAT Prep today?

If k is a common multiple of 75, 98, and 140, which of the following statements must be true?...............

During the test I did not think that 0 could be a multiple of these numbers and assumed that their LCM would the smallest multiple (and hence got this question right!) but now as I think that 0 could be a multiple of each of 75, 98, and 140, I don’t know whether to feel happy or sad.

I was wondering whether this is GMAC’s mistake or whether GMAC is consistent with this in other questions?

[Sage Pearce-Higgins]

You were right to think like that: GMAT treats multiples of a number as the number multiplied by 1, 2, or any greater integer. I've never seen a GMAT problem deal with 0 (or negative numbers) in connection with multiples. They're pretty careful to avoid that kind of nit-picking.

On a wider point, if 0 was treated as a multiple of a number, then the LCM of any numbers would be 0, so that LCM wouldn't mean anything useful.

[PrashantS209]

makes sense! thanks.

[Sage Pearce-Higgins]

Good to hear it. You're welcome.