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With the problem, "Can you find 3 consecutive numbers where the first is a multiple of 2, the second is a multiple of 3 and the third is a multiple of 4?" you know that the first example of this is 2, 3 and 4 themselves. From here you could try going through all the numbers until you reach another example of this but it takes too long. The next example could be in the thousands or millions or even billions. We need an approach that is easy to work out mathematically rather than guess work. Let's say you only knew your 2 and 3 times table. 6 is in both tables so you add 6 onto 2 and 3 to get your next pair of numbers that are consecutive and the first is a multiple of 2 and the second is a multiple of 3 (8 and 9). This works for any question which says "Can you find x consecutive numbers...". So when you are working with the numbers 2,3 and 4, you have to find the lowest common multiple of all 3 numbers which in this case is 12. Therefore you add 12 to all the numbers to get the next set of numbers that work; 14,15 and 16. If you keep adding 12 onto the numbers, all the sets of numbers work; 26, 27, 28 for example. This works because if you know a certain amount of times tables, (Let's say 2,3,4 and 5) patterns of what is divisible by these numbers repeat after you go over the lowest common multiple of a set of numbers. In this case 2,3,4 and 5 go into 60 so to get the next set of numbers that follow the criteria, you add 60, getting 62, 63, 64 and 65. 62 is divisible by 2, 63 is divisible by 3, 64 is divisible by 4 and 65 is divisible by 5, so it works. This method works for any amount of consecutive numbers e.g. 5 or 6 or 7 or even more consecutive numbers. The sets of numbers that follow the criteria are just further apart from each other.