LCM( 36, 32, 45 ) = 1440
Step 1: Write down factorisation of each number:
36 = 2 · 2 · 3 · 3
32 = 2 · 2 · 2 · 2 · 2
45 = 3 · 3 · 5
Step 2 : Match primes vertically:
36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
45 | = | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||||
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
45 | = | 3 | · | 3 | · | 5 | ||||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 1440 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.