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Which number is a multiple of three and a multiple of seven?
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Let’s start with 18.
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We know that three times six equals 18, and that means 18 is a multiple of three.
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In order for 18 to be a multiple of seven, seven times some whole number must equal 18.
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Seven times two equals 14, and seven times three equals 21.
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There is no whole number we can multiply seven by to equal 18, and that means 18 is not a multiple of three and seven.
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Next step, let’s think about three.
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Can the number three be a multiple of seven?
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Three is not a multiple of seven.
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What about 49?
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Seven times seven equals 49.
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Is there anything we can multiply by three to equal 49?
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No, 49 is not a multiple of three; it’s only a multiple of seven.
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What about 42?
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Seven times six equals 42.
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42 is a multiple of seven, and six is a multiple of three.
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That means 42 is also divisible by three.
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Three times 14 equals 42, which means 42 is a multiple of three and a multiple of seven.
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If you didn’t remember all of these multiplication facts, another way to find the multiples of three and seven is to list them out.
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Three times one is three; three times two is six; and keep going: nine, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42.
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And for seven, seven times one is seven; seven times two is 14, 21, 28, 35, 42.
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42 is a multiple of seven and three.
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We also notice that 21 is a multiple of seven and three.
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But 21 wasn’t in our box, only 42 was, which makes our final answer 42.