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Home >> L.C.M >> Prime Factorisation Method >>

## Prime Factorisation Method (LCM)

 Prime Factorisation Method Division Method

Before you learn How to calculate LCM by Prime Factorisation Method ?
you must know What is Prime Factorisation ?

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 Factors 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 Factors 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.