LCM( 12, 84, 91 ) = 1092
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
84 = 2 · 2 · 3 · 7
91 = 7 · 13
Step 2 : Match primes vertically:
12 | = | 2 | · | 2 | · | 3 | ||||
84 | = | 2 | · | 2 | · | 3 | · | 7 | ||
91 | = | 7 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
12 | = | 2 | · | 2 | · | 3 | ||||||
84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||
91 | = | 7 | · | 13 | ||||||||
LCM | = | 2 | · | 2 | · | 3 | · | 7 | · | 13 | = | 1092 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.