LCM( 56, 155, 300 ) = 130200
Step 1: Write down factorisation of each number:
56 = 2 · 2 · 2 · 7
155 = 5 · 31
300 = 2 · 2 · 3 · 5 · 5
Step 2 : Match primes vertically:
56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||||
155 | = | 5 | · | 31 | ||||||||||||
300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||||||
155 | = | 5 | · | 31 | ||||||||||||||
300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 7 | · | 31 | = | 130200 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.