LCM( 25, 40, 75 ) = 600
Step 1: Write down factorisation of each number:
25 = 5 · 5
40 = 2 · 2 · 2 · 5
75 = 3 · 5 · 5
Step 2 : Match primes vertically:
25 | = | 5 | · | 5 | ||||||||
40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||
75 | = | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
25 | = | 5 | · | 5 | ||||||||||
40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||
75 | = | 3 | · | 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.