LCM of a number

the answer is 360 not 720

I'm not sure the above replies addressed your precise question, so I'll try to explain in a different way:

The question asks: "If x is divisible by 8,12, and 45, what is the largest number that x *must* be divisible by?" This is really saying: "if the only thing you know about x is that it is divisible by 8, 12 and 45, what is the largest number you can be completely sure x is divisible by?" Of course, you're right that x could be equal to 720, and then as you say, x would be divisible not only by 360, but also by the larger number 720. But you can't be sure that x is 720, so you can't be sure that x is divisible by 720. Here x could be lots and lots of different numbers -- it might be the case that x = 360, for example, or that x = 1080, among an infinitude of possibilities.

But even though there is an infinite number of possible values of x here, no matter what x is, you can be completely certain that x is divisible by 360.

It's not actually the math that you're having a hard time with! The math is completely correct:

- You're correct that you need to find the LCM of 8, 12, and 45;
- You've correctly calculated the LCM as 360;
- 360 is the correct answer to the question.

The only issue here is in the wording of the problem. It says 'what is the largest number that x must be divisible by.' In other words, x is some number that's divisible by 8, 12, and 45. That means x could be 360, but x could also be 720, 1080, or a lot of other numbers.

You want to know the largest number that all of those possible values are divisible by - in other words, the number that x must be divisible by. x doesn't have to be divisible by 720, since x could be 360, and 360 isn't divisible by 720. But x does have to be divisible by 360.

true answer is 360....

Coincidentally, you would not believe, I had the precise same doubt yesterday.The answer could be infinity.But I hope you got the concept behind that question!!!!