Understanding Prime Factors, HCF, and LCM in Mathematics
Explore the concepts of Prime Factors, Highest Common Factor (HCF), and Lowest Common Multiple (LCM) through engaging Venn diagrams and examples. Learn how to calculate HCF and LCM for numbers like 12 & 18, 50 & 80, and 105 & 42 using prime decomposition. Enhance your math skills efficiently!
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Presentation Transcript
From last lesson: What is the highest common factor of 12 & 18? 2 3 2 2 3 ??? = 6 3 What is the lowest common multiple of 12 & 18? 2 2 3 3 ??? = 36
Here is a Venn Diagram Where is the number 12 represented in this Venn Diagram? 2 2 3 Where is the number 18 represented in this Venn Diagram? 3
The HCF of 12 & 18 is 6 Can you see where this is represented in the Venn Diagram? 2 2 3 3
The LCM of 12 & 18 is 36 Can you see where this is represented in the Venn Diagram? 2 2 3 3
Prime Factors and Venn Diagrams I DO WE DO YOU DO For each Venn Diagram below, write down: a) The two numbers represented b) The LCM c) The HCF a) Write down the two numbers represented by the Venn Diagram above. a) Write down the two numbers represented by the Venn Diagram above. b) Write down the LCM for these two numbers. b) Write down the LCM for these two numbers. c) Write down the HCF for these two numbers. c) Write down the HCF for these two numbers.
Prime Decomposition, HCF and LCM What is the HCF and LCM of 50 and 80? Start by finding the Prime Decomposition of both on your whiteboards
Prime Decomposition, HCF and LCM What is the HCF and LCM of 50 and 80? 50 = 2 x 5 x 5 80 = 2 x 2 x 2 x 5 x 2 Numbers common to both 50 and 80 go in the middle 50 80 Use a Venn diagram 2 5 5 2 2 2 HCF Multiply the middle numbers LCM Multiply all the numbers 2 x 5 = 10 5 x 5 x 2 x 2 x 2 x 2 = 400
Prime Decomposition, HCF and LCM Work out the HCF and LCM of 105 and 42 Start by finding the Prime Decomposition of both on your whiteboards
Prime Decomposition, HCF and LCM What is the HCF and LCM of 105 and 42? 105 = 3 x 5 x 7 42 = 2 x 3 x 7 Numbers common to both 105 and 42 go in the middle 105 42 Use a Venn diagram 2 5 3 7 HCF Multiply the middle numbers LCM Multiply all the numbers 3 x 7 = 21 2 x 3 x 5 x 7 = 210
Further Practice Using Prime Factorisation find the HCF and the LCM of: 36 and 40 50 and 90 45 and 80 120 and 300 125 and 300 180 and 900
Mark and correct your work Using Prime Factorisation find the HCF and the LCM of: 36 and 40 HCF = 4, LCM = 360 50 and 90 HCF = 10, LCM = 450 45 and 80 HCF = 5, LCM = 720 120 and 300 HCF = 30, LCM = 600 125 and 300 HCF = 25, LCM = 1500 180 and 900 HCF = 180, LCM = 900
CHALLENGE Place the factors for a2b2c2 and ab2c into this Venn diagram a2b2c2 ab2c What is the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of a2b2c2 and ab2c?
