LCM( 21, 28, 24 ) = 168
Step 1: Write down factorisation of each number:
21 = 3 · 7
28 = 2 · 2 · 7
24 = 2 · 2 · 2 · 3
Step 2 : Match primes vertically:
21 | = | 3 | · | 7 | ||||||
28 | = | 2 | · | 2 | · | 7 | ||||
24 | = | 2 | · | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
21 | = | 3 | · | 7 | ||||||||
28 | = | 2 | · | 2 | · | 7 | ||||||
24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 7 | = | 168 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.