Find the HCF and LCM of given numbers Write a number as a product of its prime factors Key Words common factor multiple highest prime product 07092020 CONTENTS Click to go to HCF AND LCM ID: 1043860
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1. Starter:07/09/2020L.O. To be able toFind the HCF and LCM of given numbersWrite a number as a product of its prime factorsKey Wordscommon, factor, multiple, highest, prime, product
2. 07/09/2020CONTENTS – Click to go to…HCF AND LCMLCM WORDED PROBLEMSPRODUCT OF PRIME FACTORSUSING PRODUCT OF PRIMES TO FIND HCF AND LCM
3. 07/09/2020HCF AND LCM
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5. DefinitionThe Highest Common Factor of two numbers is the largest number that is a common factor of both numbers. We call it the HCF.List all factors of each number List them in pairs so you won’t miss any out!Circle all common factorsThe highest circled number is the HCF07/09/2020
6. 07/09/2020ExampleFind the HCF of 24 and 30Factors of 24:Factors of 30:So the HCF of 24 and 30 is:
7. 07/09/2020ExampleFind the HCF of 36 and 45Factors of 36:Factors of 45:So the HCF of 36 and 45 is:
8. TaskFind the HCF of the following numbers...8 and 12 e) 36 and 5420 and 30 f) 18 and 2412 and 18 g) 36 and 4821 and 35 h) 56 and 24Then challenge your partner to find the HCF of two numbers of your choice... how well do they do?07/09/2020
9. 07/09/2020Find the HCF of the sets of numbers shown.HCF 9 and 15HCF 12 and 30HCF 18 and 4HCF 20 and 35HCF 42 and 28HCF 36 and 27HCF 9, 54, 18HCF 24, 56, 16HCF 60, 36, 2436251499812abcdefghi
10. DefinitionThe Lowest Common Multiple of two numbers is the smallest number that is a common multiple of both numbers. We call it the LCM.List the first few multiples of each number Circle the common multiplesThe lowest circled number is the LCM07/09/2020
11. Multiples of 6Multiples of 824487296816324056648088104 …6121824303642485460667278849096102…07/09/2020
12. 07/09/2020ExampleFind the LCM of 8 and 10Multiples of 8:Multiples of 10:So the LCM of 8 and 10 is:
13. 07/09/2020ExampleFind the LCM of 20 and 25Multiples of 20:Multiples of 25:So the LCM of 20 and 25 is:
14. 07/09/2020Find the LCM of the sets of numbers shown.LCM 2 and 3LCM 4 and 10LCM 6 and 18LCM 9 and 36LCM 7 and 9LCM 36 and 12LCM 9, 54, 18LCM 14, 28, 7LCM 5, 6, 7620183663365428210abcdefghi
15. TaskFind the LCM of the following numbers...4 and 10 e) 9 and 64 and 5 f) 7 and 55 and 9 g) 6 and 812 and 3 h) 6 and 7Can you find the LCM of these harder numbers?10 and 1520 and 3012 and 2007/09/2020
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18. Discussion task questionsWhy do we find the HIGHEST common factor, but then the LOWEST common multiple?Can you think of examples of other maths topics where we could use the HCF or LCM to help us07/09/2020
19. 07/09/2020USING THE LCM TO SOLVE WORDED PROBLEMS
20. 07/09/2020LCM worded problemsOften a question will need you to find the LCM without explicitly using those words. Examples are…Buying two or three different products that come in different sized packets, but wanting to buy the same amount of each productA situation where two things leave a place at the same time and you need to find the next time when they are all there together (busses or trains leaving the station, racers being at the start line of a race track, etc)
21. LCM worded problems - Step by stepLIST the first few amounts for each of the different things in the questionKeep checking carefully to see if there are any common values in the lists!Add more to the lists until you find a value that’s in commonRead and make sure that you answered the question correctly in the context givenExampleRita is going to make some cheeseburgers for a party.She buys some packets of cheese slices and some boxes of burgers.There are 20 cheese slices in each packet.There are 12 burgers in each box.Rita buys exactly the same number of cheese slices and burgers.How many packets of cheese slices and how many boxes of burgers does she buy?07/09/2020Cheese slices: 20, 40, 60, 80, 100Burgers: 12, 24, 36, 48, 60So I need 3 packets of cheese slices, and 5 boxes of burgers
22. 07/09/2020Exam question
23. 07/09/2020Mark scheme
24. 07/09/2020Some to try!These are some past paper questions on this theme that are worth having a go at, to test your skills…
25. 07/09/2020PRODUCT OF PRIME FACTORS
26. Key phrasesYou could be asked to find the “product of prime factors” or the “prime factor decomposition” of a number. Both of these phrases mean the same thing.Step by stepDraw a factor treeWrite out all the PRIME factors as a list, with a MULTIPLY symbol in between each number (a product of prime factors!)07/09/2020
27. 180101807/09/2020Think of any pair of numbers that multiply to make 180
28. 180101807/09/2020Think of factor pairs for both 10 and 18
29. 1052180186307/09/2020
30. 235102618018307/09/2020When you get to a PRIME number, circle it and stop that branch
31. ExampleWrite 75 as a product of prime factors07/09/2020
32. ExampleWrite120 as a product of prime factors07/09/2020
33. TaskWrite the following numbers as a product of their prime factors20327219526130330604507/09/2020
34. SHORTCUT!!!A quick way to find the product of prime factors can be done on your calculator…ExampleWrite 36 as a product of prime factorsType in 3 6 =Press shift then press ᵒ’ ’’ (says FACT above the button)Your screen will show the number as a product of its prime factors!07/09/2020
35. 07/09/2020USING PRODUCT OF PRIMES TO FIND HCF AND LCM
36. Using the product of prime factors to find the HCFFind the product of primes for each numberCircle pairs that are in BOTH listsMultiply these paired numbers togetherThe result is the HCFUsing the product of prime factors to find the LCMFirst find the HCF as aboveFind all the “leftover” numbers (that didn’t pair up)Times all the leftovers by the HCFThe result is the LCMSome interactive examples can be found here07/09/2020
37. Find the Highest Common Factor of 36 and 90 36236623 90251093336 = 2 2 3 390 = 2 3 3 507/09/2020
38. The common prime factors are 2 3 3HCF = 1836 = 2 2 3 390 = 2 3 3 507/09/2020
39. Find the Highest Common Factor of 18 and 60 HCF = 2 3HCF = 618 = 2 3 360 = 2 2 3 5Multiply the common prime factors07/09/2020
40. Find the Highest Common Factor of 315 and 525 HCF = 3 5 7HCF = 105315 = 3 3 5 7525 = 3 5 5 7Multiply the common prime factors07/09/2020
41. Find the Lowest Common Multiple of 36 and 81 36236623 81339936 = 2 2 3 381 = 3 3 3 3 3307/09/2020
42. = 32481 = 3 3 3 3LCM = 2 2 3 336 = 2 2 3 33 3 HCF 907/09/2020
43. Finding the LCM LCM = 2 2 3= 246 = 2 38 = 2 2 2 2 HCF 207/09/2020
44. Find the Lowest Common Multiple of 18 and 60= 18060 = 2 2 3 5LCM = 2 3 518 = 2 3 32 3 HCF x 607/09/2020
45. Find the Lowest Common Multiple of 24 and 40= 12040 = 2 2 2 524 = 2 2 2 3LCM = 3 52 2 2 HCF 807/09/2020
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48. Using the product of prime factors and a VENN diagramYou can also put your products of prime factors in a Venn diagram, and use that to help you to calculate the HCF and LCM…HCF – multiply only the numbers in the overlapping middle sectionLCM – multiply all the numbers you can see in the Venn diagram07/09/2020
49. 6029460 = 2 × 2 × 3 × 5294 = 2 × 3 × 7 × 7223577HCF of 60 and 294 =2 × 3 = 6LCM of 60 and 294 = 2 × 5 × 2 × 3 × 7 × 7 =294007/09/2020
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