LCM( 405, 783, 513 ) = 223155
Step 1: Write down factorisation of each number:
405 = 3 · 3 · 3 · 3 · 5
783 = 3 · 3 · 3 · 29
513 = 3 · 3 · 3 · 19
Step 2 : Match primes vertically:
405 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | ||||
783 | = | 3 | · | 3 | · | 3 | · | 29 | ||||||
513 | = | 3 | · | 3 | · | 3 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
405 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | ||||||
783 | = | 3 | · | 3 | · | 3 | · | 29 | ||||||||
513 | = | 3 | · | 3 | · | 3 | · | 19 | ||||||||
LCM | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 19 | · | 29 | = | 223155 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.