LCM( 15, 20, 38 ) = 1140
Step 1: Write down factorisation of each number:
15 = 3 · 5
20 = 2 · 2 · 5
38 = 2 · 19
Step 2 : Match primes vertically:
15 | = | 3 | · | 5 | ||||||
20 | = | 2 | · | 2 | · | 5 | ||||
38 | = | 2 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
15 | = | 3 | · | 5 | ||||||||
20 | = | 2 | · | 2 | · | 5 | ||||||
38 | = | 2 | · | 19 | ||||||||
LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 19 | = | 1140 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.