Mon June 02, 2008 By: Rohan Raja

How to find the HCF and LCM of given THREE numbers without factorisation?(using Euclid's Lemma)

Expert Reply
Fri July 25, 2008

HCF of given three numbers can be found out using lemma. Take any of two numbers.Apply lemma to both.If remainder is not zero,apply lemma again to the divisor and remainder again.Continue this process with last divisor and remainder till the remainder turns zero.The last divisor will be HCF of two numbers. Find next the HCF of above HCF and the third number applying lemma.

                                      Remember LCM can not be found using lemma.

For this purpose, we have formula

                                                p.q.r. HCF(p,q,r)

                  LCM(p,q,r) = ------------------------------------------------     

                                           HCF(p,q). HCF(q,r).HCF(p,r)

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