LCM( 1080, 120, 1560 ) = 14040
Step 1: Write down factorisation of each number:
1080 = 2 · 2 · 2 · 3 · 3 · 3 · 5
120 = 2 · 2 · 2 · 3 · 5
1560 = 2 · 2 · 2 · 3 · 5 · 13
Step 2 : Match primes vertically:
1080 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | ||
120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||
1560 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
1080 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | ||||
120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||||
1560 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 13 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 13 | = | 14040 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.