Efficient Procedures for HCF and LCM

Transcript

Efficient Procedures for HCF and LCMWe use a more efficient method for finding HCF and LCM For HCF Instead of finding Prime Factorisation for two numbers separately, we find it together. Example: Here, we stop at 7 & 15 since they do not have any common factor left. ∴ HCF = 2 × 2 × 3 For LCM We do the same thing for LCM Example: For LCM, we multiply all the numbers ∴ LCM = 2 × 2 × 3 × 7 × 15 Let’s do some more examples For 300 & 150 For 630 & 770 Guna and Anshu's Shortcut Guna and Anshu discover something cool. You don't have to use small prime numbers like 2,3 , or 5 if you can see a bigger number! Guna's Trick: For 300 and 150 , he saw immediately that 50 goes into both. He divided by 50 in one step. Anshu's Trick: For 630 and 770 , she saw that 10 goes into both (because they end in 0 ). Is this allowed? Yes! As long as the number divides both numbers perfectly, you can use it. It makes the ladder shorter and faster.