Algebra Den

Prime Factorisation Method (LCM)

Before you learn How to calculate LCM by Prime Factorisation Method ? you must know What is Prime Factorisation (Topic already available in this site) Under Prime Factorisation Method, LCM = Product of Prime factors which occurs maximum time in any given number. Following examples can guide you How to calculate LCM by Prime Factorisation Method ? Example = 1 By using Prime Factorisation Method, find the LCM of 24 & 18 ? Answer = Prime Factorisation of given numbers are as:- 24 = 2 × 2 × 2 × 3. 18 = 2             × 3 × 3. In the above Prime Factorisation, Maximum number of times 2 occurs is three(in given number 24) and Maximum number of times 3 occurs is two(in given number 18) LCM = Product of Prime factors which occurs maximum time in any given number         = (Maximum number of times 2 occurs) × (Maximum number of times 3 occurs)         = (2 × 2 × 2) × (3 × 3)         = 8 × 9     = 72. Hence, LCM of 28 & 18 = 72 Example = 2 Find the LCM of 20, 30,& 40 by Prime Factorisation Method ? Answer = Prime Factorisation of given numbers are as:- 20 = 2 × 2             × 5. 30 = 2             × 3 × 5. 40 = 2 × 2 × 2       × 5. In the above Prime Factorisation, Maximum number of times 2 occurs is three(in given number 40), 3 occurs only once(in given number 30) and 5 occurs once in all the given numbers. LCM = Product of Prime factors which occurs maximum time in any given number         = (Maximum number of times 2 occurs) × (Maximum number of times 3 occurs) × (Maximum number of times 5 occurs)         = (2 × 2 × 2) × (3) × (5)         = 8 × 3 × 5     = 120. Hence, LCM of 28 & 18 = 120.