LCM( 30, 74, 80 ) = 8880
Step 1: Write down factorisation of each number:
30 = 2 · 3 · 5
74 = 2 · 37
80 = 2 · 2 · 2 · 2 · 5
Step 2 : Match primes vertically:
30 | = | 2 | · | 3 | · | 5 | ||||||||
74 | = | 2 | · | 37 | ||||||||||
80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
30 | = | 2 | · | 3 | · | 5 | ||||||||||
74 | = | 2 | · | 37 | ||||||||||||
80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 37 | = | 8880 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.