LCM( 150, 200, 500 ) = 3000
Step 1: Write down factorisation of each number:
150 = 2 · 3 · 5 · 5
200 = 2 · 2 · 2 · 5 · 5
500 = 2 · 2 · 5 · 5 · 5
Step 2 : Match primes vertically:
150 | = | 2 | · | 3 | · | 5 | · | 5 | ||||||
200 | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | ||||
500 | = | 2 | · | 2 | · | 5 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
150 | = | 2 | · | 3 | · | 5 | · | 5 | ||||||||
200 | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | ||||||
500 | = | 2 | · | 2 | · | 5 | · | 5 | · | 5 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 5 | = | 3000 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.