LCM( 68, 72, 90 ) = 6120
Step 1: Write down factorisation of each number:
68 = 2 · 2 · 17
72 = 2 · 2 · 2 · 3 · 3
90 = 2 · 3 · 3 · 5
Step 2 : Match primes vertically:
68 | = | 2 | · | 2 | · | 17 | ||||||||
72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
90 | = | 2 | · | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
68 | = | 2 | · | 2 | · | 17 | ||||||||||
72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 17 | = | 6120 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.