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