LCM( 40, 48, 45 ) = 720
Step 1: Write down factorisation of each number:
40 = 2 · 2 · 2 · 5
48 = 2 · 2 · 2 · 2 · 3
45 = 3 · 3 · 5
Step 2 : Match primes vertically:
40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||
48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
45 | = | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||
48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
45 | = | 3 | · | 3 | · | 5 | ||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 720 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.