LCM( 54, 42, 63 ) = 378
Step 1: Write down factorisation of each number:
54 = 2 · 3 · 3 · 3
42 = 2 · 3 · 7
63 = 3 · 3 · 7
Step 2 : Match primes vertically:
54 | = | 2 | · | 3 | · | 3 | · | 3 | ||
42 | = | 2 | · | 3 | · | 7 | ||||
63 | = | 3 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||
42 | = | 2 | · | 3 | · | 7 | ||||||
63 | = | 3 | · | 3 | · | 7 | ||||||
LCM | = | 2 | · | 3 | · | 3 | · | 3 | · | 7 | = | 378 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.