Question

Find the LCM of 20 and 25 by prime factorisation method

Answer 1

The least common multiple or LCM or LCD. There are two methods to find lcm.
A) Lcm prime factorization
B) By using multiples.
The lowest common multiple of two or more given numbers is the lowest (or smallest or least) of their common multiples. 
By individual prime factors
1) LCM prime factorization : In this method use prime numbers find the factors of the given numbers individually. Multiplication of all the prime numbers gives you the LCM.
Example 1: Find the LCM of 12 and 18 
Solution:The prime factorization of 12 and 18 are : 
12 = 2 x 2 x 3 
18 = 2 x 3 x 3 
In these LCM prime factorization, the maximum number of times the prime factor 2 occurs is two; this happens for 12. Similarly , the maximum number of times the factor 3 occurs is two; this happens for 18. The LCM of the two numbers is the product of prime factors counted the maximum number of times they occur in any of the numbers. Thus in this case 
LCM = 2 x 2 x 3 x 3 = 36
Example 2 : Find the LCM of 24 and 90.
Solution : The prime factorization of 24 and 90 are : 

24 = 2 x 2 x 2 x 3 
90 = 2 x 3 x3 x 5 
In these prime factorizations the maximum number of times the prime factor 2 occurs is three; this is for 24. And the maximum number of times the prime factor 3 occurs is two; this is for 90. The prime factor 5 occurs only once in 90 .
Thus LCM of 24 and 90 is 
= (2 x 2 x 2) x ( 3 x 3 ) x 5 = 360. 

Answer 2

Steps to find LCM
I)Find the prime factorization of 20
20 = 2 × 2 × 5

ii)Find the prime factorization of 25
25 = 5 × 5

iii)Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 2 × 5 × 5

iv)LCM = 100