Understanding LCM: Prime Factors and Venn Diagrams
Explore the concept of Lowest Common Multiple (LCM) through prime factorization and Venn diagrams. Learn why LCMs must be greater, divisible by certain numbers, and how to find LCMs of various numbers efficiently.
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Three buses arrive at this bus stop at 5pm. When is the next time there will be three buses at the bus stop?
80 = 2 x 2 x 2 x 2 x 5 60 = 2 x 2 x 2 x 3 x 5 Prime factors can also be used to find the LCM of two or more numbers. Why must the LCM of 60 and 80 be greater than 80?
80 = 2 x 2 x 2 x 2 x 5 60 = 2 x 2 x 2 x 3 x 5 Why must the LCM of 60 and 80 be divisible by 3? ??? = 2 2 2 2 5 3 80
80 = 2 x 2 x 2 x 2 x 5 60 = 2 x 2 x 2 x 3 x 5 Why must the LCM of 60 and 80 be divisible by 16? ??? = 2 2 3 5 2 2 60
By using a Venn Diagram it can be seen that the LCM of 60 and 80 is 2 2 2 2 3 5 = ??? ? ? ? ? ? ?
Find the Lowest Common Multiple (LCM) of 12 & 20. Complete Prime Factorisation for both numbers. Input the Prime Factors into a Venn diagram Shared Factors 20 12 20 12 3 5 2 10 2 2 6 2 2 5 2 3 LCM = Product of all factors in the diagram 12 = 2 2 3 2 2 3 5 = 60 20 = 2 2 5
Find the Lowest Common Multiple (LCM) of 18 & 45. Complete Prime Factorisation for both numbers. Input the Prime Factors into a Venn diagram Shared Factors 45 18 45 18 2 3 15 2 9 5 3 3 3 5 3 3 LCM = Product of all factors in the diagram 18 = 2 3 3 2 3 3 5 = 90 45 = 3 3 5
Find the Lowest Common Multiple (LCM) of 24 & 36. Complete Prime Factorisation for both numbers. Input the Prime Factors into a Venn diagram Shared Factors 36 24 36 24 2 2 2 18 3 2 12 2 3 2 9 2 6 3 3 2 3 LCM = Product of all factors in the diagram 24 = 2 2 2 3 2 2 2 3 3 = 72 36 = 2 2 3 3
Find the Lowest Common Multiple (LCM) of 75 & 90. Complete Prime Factorisation for both numbers. Input the Prime Factors into a Venn diagram Shared Factors 90 75 90 75 2 5 2 45 3 3 25 3 5 5 9 5 5 3 3 LCM = Product of all factors in the diagram 75 = 3 5 5 2 3 3 5 5 = 450 90 = 2 3 3 5
Title: Using Prime Factorisation to work out LCM Work out the LCM of: 100 & 120 120 & 180 150 & 180 150 & 75 100 & 180 100 & 75 120 & 75 180 & 75 Two buses leave Aspley Lane at 9am. Bus A leaves every 18 minutes, and Bus B leaves every 27 minutes. What will be the next time the buses leave Aspley Lane at the same time?
Mark your work Work out the LCM of: 100 & 120 = 600 120 & 180 = 360 150 & 180 = 900 150 & 75 = 150 100 & 180 = 900 100 & 75 = 300 120 & 75 = 600 180 & 75 = 900 Two buses leave Aspley Lane at 9am. Bus A leaves every 18 minutes, and Bus B leaves every 27 minutes. What will be the next time the buses leave Aspley Lane at the same time?
18 = 2 3 3 1) Complete Prime Factorisation for both numbers. 24 = 2 2 2 3 24 18 2 2 3 2) Input the Prime Factors into a Venn diagram. 3 2 2 2 2 3 3 = 72 3) LCM = Product of all factors in the diagram Find the Lowest Common Multiple (LCM) of these pairs of numbers. a) 20 & 30 a) 54 & 36 a) 80 & 300 LCM = b) 12 & 18 & 90 b) 12 & 40 b) 80 & 24 LCM = c) 80 & 150 & 180 c) 18 & 45 c) 90 & 150 LCM =
18 = 2 3 3 1) Complete Prime Factorisation for both numbers. 24 = 2 2 2 3 24 18 2 2 3 2) Input the Prime Factors into a Venn diagram. 3 2 2 2 2 3 3 = 72 3) LCM = Product of all factors in the diagram Find the Lowest Common Multiple (LCM) of these pairs of numbers. a) 20 & 30 a) 54 & 36 a) 80 & 300 LCM = 1200 LCM = 60 LCM = 108 b) 12 & 18 & 90 LCM = 180 b) 12 & 40 b) 80 & 24 LCM = 120 LCM = 240 c) 80 & 150 & 180 LCM = 3600 c) 18 & 45 c) 90 & 150 LCM = 450 LCM = 90
Challenge Work out the smallest integer that is a multiple of 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10
