Hi! My name is Stephanie. I am a student and I'm in grade 8.

I was came across this question while doing my homework and I didn't know how to do it. Could you please help me out with it? Here it is:

How many of the first 1000 positive integers are multiples of all four of the numbers 2, 3, 4, and 5.

It seemed easy at first, but then I got confused. I would like to know what would be the simplest way of doing this. Please write back if you can! Thank you very much.


Hi Stephanie,

What is the smallest number that is a multiple of 2, 3, 4 and 5? Suppose that we call this number N. Multiples of all four numbers 2, 3, 4 and 5 must then be multiples of N. That is they are the numbers

1 N
2 N
3 N
How many of these do you need to arrive at a number larger than 1000?


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