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Factors and Multiples (Lowest Common Multiple) Name: ( ) Worksheet 6 Class: Points to Note: To find L.C.M of 3 or more numbers, the method used is almost the same. Example: Find the lowest common multiple of 420, 63 and 126. Method 1: (Prime Factorisation) Step 1: Factorise all numbers into prime factors. 2 420 = 2 × 3 × 7 × 5 32 × 7 63 = 2 126 = 2 × 3 × 7 Page 22 By: Mr Wong Han Ming Step 2: Look at all the indiviual prime numbers and select the biggest number from each group. 2 420 = 2 × 3 × 7 × 5 32 × 7 63 = 2 126 = 2 × 3 × 7 2 420 = 2 × 3 × 7 × 5 32 × 7 63 = 2 126 = 2 × 3 × 7 For the number 2, 22 is biggest among the group. For the number 3, 32 is biggest among the group. 2 420 = 2 × 3 × 7 × 5 32 × 7 63 = 2 126 = 2 × 3 × 7 2 420 = 2 × 3 × 7 × 5 32 × 7 63 = 2 126 = 2 × 3 × 7 For the number 7, there is only one option, which is 7, so it is considered the biggest number. Step 3: For the number 5, there is only one option, which is 5, so it is considered the biggest number. Multiply the selected numbers to get the L.C.M 2 420 = 2 × 3 × 7 × 5 32 × 7 63 = 2 126 = 2 × 3 × 7 select the biggest number 2 2 L.C.M = 2 × 3 × 7 × 5 = 1 260 Page 23 By: Mr Wong Han Ming Method 2: (Continuous Division) Step 1: Find a prime number that can divide all numbers. 3 420 140 63 21 126 42 3 420 7 140 20 63 21 3 126 42 6 3 420 7 140 2 20 10 63 21 3 3 126 42 6 3 (For example, 420, 63 and 126 can be divided by 3 to get 140, 21 and 42) Step 2: Repeat step 1 for the next line of numbers. (For example, 140, 21 and 42 can be divided by 7 to get 20, 3 and 6) Step 3: Repeat step 2 until there is no more common factor. Step 4: If there is a common factor between TWO numbers, divide the two numbers by the factor and leave the rest of the numbers alone. (For example, 20 and 6 can be divided by 2 to get 10 and 3) leave this number alone Step 5: Repeat step 4 until there is no more common factor between two numbers. 3 420 7 140 2 20 3 10 10 63 21 3 3 1 126 42 6 3 1 Step 4: Multiplying the circled numbers, we find the L.C.M to be 3 420 7 140 2 20 3 10 10 63 21 3 3 1 126 42 6 3 1 L.C.M = 3 × 7 × 2 × 3 × 10 × 1 × 1 = 1 260 Page 24 By: Mr Wong Han Ming Practice: Find the lowest common multiple of the following. 1) 8, 16 and 18 2) 18, 15 and 24 3) 8, 12 and 36 4) 42, 36 and 24 5) 20, 45 and 60 6) 54, 81 and 108 4) 5) 6) 504 180 324 Answers: 1) 2) 3) 144 360 72 Page 25 By: Mr Wong Han Ming