LCM( 56, 96, 404 ) = 67872
Step 1: Write down factorisation of each number:
56 = 2 · 2 · 2 · 7
96 = 2 · 2 · 2 · 2 · 2 · 3
404 = 2 · 2 · 101
Step 2 : Match primes vertically:
56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||||
96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
404 | = | 2 | · | 2 | · | 101 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||||||
96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
404 | = | 2 | · | 2 | · | 101 | ||||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 7 | · | 101 | = | 67872 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.