Identify the first three common multiples of three and seven.
Well, before we can identify common multiples, we just need to find the multiples of both three and seven. We’ll list the multiples of three starting with three times one, three. Three times two, six. Three times three is nine. Three times four is 12. The next multiple is 15, then 18, 21, 24, 27, and 30.
Let’s stop here and look for some of the multiples of seven starting with seven times one, which is seven. Seven times two, 14. Seven times three, 21. Seven times four is 28. Next, we have 35, 42, 49, 56, 63, and 70.
So we found the first 10 multiples of three and seven. Now we need to look and see if they share any multiples, if they have any in common. We notice that in our list, three and seven both have a common multiple of 21. But that’s the only shared multiple on this list. We only found our multiples of three up to 30, while we found our multiples of seven up to the number of 70. So we probably should look for a few more multiples of three.
We stopped here with three times 10. So we’ll carry on with three times 11, 33, 36. And you can recognize that we’re adding three each time, 39, 42. But at 42 I remember that seven times six is 42. So we found another shared multiple, another common multiple.
Okay, now we have two common multiplies, but we’re looking for the first three. So we have to keep going, 45, 48, 51, 54, 57. Still haven’t found another match, 60, 63. Okay, seven times nine is 63. 63 is a multiple of both seven and three.
Our first three common multiples of three and seven are 21, 42, and 63.