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Which of the following pairs of numbers has a common multiple of 24?
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Five and two, six and 11, two and 12, or seven and 17.
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When we say a number has a multiple of 24, what we mean is that if we add that number several times we’ll eventually reach the number 24.
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So 24 is a multiple of that particular number.
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24 is in the times table for that number.
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One of the pairs of numbers that we’re given has a common multiple of 24.
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In other words, both numbers have 24 in their times table.
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Another way of thinking about this problem is understanding that if a number has a multiple of 24, it must be a factor of 24.
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So finding the factors of 24 might be a good place to start with this problem.
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Let’s identify them.
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A quick way to make sure that we find all the factors of a number is to try and think of them in pairs.
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Which pairs make 24?
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One multiplied by 24 equals 24.
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And so both one and 24 are factors of 24.
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Two multiplied by 12 equals 24.
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So we can include the factors two and 12 in our list.
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Three eights are 24.
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And finally, four sixes are 24 too.
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So the full list of factors of 24 is one, two, three, four, six, eight, 12, and 24.
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Each of these numbers has 24 as one of its multiples.
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Let’s use our list of factors to look at each pair of numbers that we’ve been given.
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Is there a pair where both numbers are factors of 24?
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What about five and two?
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We can see from our list that two is a factor of 24.
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So we know 24 must be a multiple of two.
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Two, four, six, eight, 10, 12, 14, 16, 18, 20, 22, 24.
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But the number five is not a factor of 24.
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This means 24 is not a multiple of five.
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Five, 10, 15, 20, 25 is the nearest we get.
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Our first pair of numbers do not have a common multiple of 24.
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What about our second pair of numbers?
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We can see that six is a factor of 24.
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This means that 24 is a multiple of six.
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Six, 12, 18, 24.
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Unfortunately, the second number in the pair 11 is not a factor of 24.
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24 is not a multiple of 11.
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In fact, we only get to 22 if we count in 11s.
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What about two and 12?
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Yes, these are both factors of 24.
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In fact, we can multiply these two numbers by each other to get 24.
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And because they’re both factors of 24, we can say that 24 is a multiple of these numbers.
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They have this in common.
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They have a common multiple of 24.
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Two, four, six, eight, 10, 12, 14, 16, 18, 20, 22, 24.
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And then if we count in 12s, 12, 24 — 24 features in both times tables.
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In our final pair of numbers, we can see that neither of them are factors of 24.
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We used our knowledge of multiples but also of factors to help us to find the correct pair of numbers.
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The pair of numbers that has a common multiple of 24 is two and 12.