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