Multiples of all four of the numbers 2, 3, 4, and 5

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.

-Stephanie

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

N
2

N
3

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

Cheers,
Penny

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