LCM( 64, 128 ) = 128
Step 1: Write down factorisation of each number:
64 = 2 · 2 · 2 · 2 · 2 · 2
128 = 2 · 2 · 2 · 2 · 2 · 2 · 2
Step 2 : Match primes vertically:
64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||
128 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||
128 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | = | 128 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.