LCM( 40, 36, 24 ) = 360
Step 1: Write down factorisation of each number:
40 = 2 · 2 · 2 · 5
36 = 2 · 2 · 3 · 3
24 = 2 · 2 · 2 · 3
Step 2 : Match primes vertically:
40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||
36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||
24 | = | 2 | · | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||
36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 360 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.