 The multiples of a positive Whole number are those numbers you get when multiplying it by 1, 2, 3, 4 ... and so on. The set of multiples is infinite. For example, here are the multiples of 18: 18, 36, 54, 72, ... etc. The LOWEST COMMON MULTIPLE of two or more numbers is the smallest number which is a multiple of all of them. For example: Find the lowest common multiple for 8 and 12: Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, ... Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ... The first four common multiples of 8 and 12 are 24, 48, 72 and 96 The lowest common multiple is 24. Here's an example with three numbers: Find the LCM for 16, 18 and 24: Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ... Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, ... Multiples of 24: 24, 48, 72, 96, 120, 144, ... The lowest common multiple is 144 You will need a calculator. Sometimes you'll need to find lots of multiples before you find the first common one! There is a quicker way to find the lowest common multiple, but you'll need to review finding a number's prime factors first. Let's look at the previous example again: Find the LCM for 16, 18 and 24: Let's find the prime factors of each number: 16: 2x2x2x2 18: 2x3x3 24: 2x2x2x3 The LCM is built from the most number of each prime factor: We need four 2's, and two 3's LCM = 2x2x2x2 x3x3 = 144 This is quicker if you know the times tables because prime factors are often small and you won't need a calculator to find them. Here's another example: Find the LCM for 8, 20, 25 and 36: Find the prime factors of each number: 8: 2x2x2 20: 2x2x5 25: 5x5 36: 2x2x3x3 LCM = 2x2x2 x3x3 x5x5 = 1800 This one would have taken a long time doing it the other way! |