LCM( 456, 696, 726 ) = 1600104
Step 1: Write down factorisation of each number:
456 = 2 · 2 · 2 · 3 · 19
696 = 2 · 2 · 2 · 3 · 29
726 = 2 · 3 · 11 · 11
Step 2 : Match primes vertically:
456 | = | 2 | · | 2 | · | 2 | · | 3 | · | 19 | ||||||
696 | = | 2 | · | 2 | · | 2 | · | 3 | · | 29 | ||||||
726 | = | 2 | · | 3 | · | 11 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
456 | = | 2 | · | 2 | · | 2 | · | 3 | · | 19 | ||||||||
696 | = | 2 | · | 2 | · | 2 | · | 3 | · | 29 | ||||||||
726 | = | 2 | · | 3 | · | 11 | · | 11 | ||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 11 | · | 11 | · | 19 | · | 29 | = | 1600104 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.