LCM( 48, 64, 120 ) = 960
Step 1: Write down factorisation of each number:
48 = 2 · 2 · 2 · 2 · 3
64 = 2 · 2 · 2 · 2 · 2 · 2
120 = 2 · 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||
120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||
64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | = | 960 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.