LCM( 20, 24, 25 ) = 600
Step 1: Write down factorisation of each number:
20 = 2 · 2 · 5
24 = 2 · 2 · 2 · 3
25 = 5 · 5
Step 2 : Match primes vertically:
20 | = | 2 | · | 2 | · | 5 | ||||||
24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
25 | = | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
20 | = | 2 | · | 2 | · | 5 | ||||||||
24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
25 | = | 5 | · | 5 | ||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | = | 600 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.