Math CentralQuandaries & Queries


Question from pat, a student:
what are the common multiples of 2 and 5, through 30, because i been working on it for hours


If you are putting that sort of time in, you would save time even by listing all the multiples of 2, then all the multiples of 5, and seeing which ones were in both lists. That's all a common multiple is - something that is both a multiple of one thing and of another.

Once you've done that, you should see a pattern. Just for fun, use that pattern to write down the common multiples of 2 and 5 through 100. [It will take you less than a minute.]

If you're really feeling like a mathematician now, see if you can figure out a fast way to write down common multiples of (say) 3 and 5.

Good Hunting!


Hi Pat. A common multiple is a number into which both of your numbers
divide evenly.

The first common multiple of 2 and 5 is 10, because that is the lowest
number that you can divide by 2 and get a whole number and you can also
divide by 5 and get a whole number. What's the next one?

One way of finding the common multiples of 2 and 5 through 30 is to
write the multiples of each through 30:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
5, 10, 15, 20, 25, 30

what's common in these lists?

Hope this helps,
Stephen La Rocque.


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