LCM( 144, 112, 418 ) = 210672
Step 1: Write down factorisation of each number:
144 = 2 · 2 · 2 · 2 · 3 · 3
112 = 2 · 2 · 2 · 2 · 7
418 = 2 · 11 · 19
Step 2 : Match primes vertically:
144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
112 | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||||||
418 | = | 2 | · | 11 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||
112 | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||||||||
418 | = | 2 | · | 11 | · | 19 | ||||||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | · | 11 | · | 19 | = | 210672 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.