Question
Find Least Common Multiple of 60, 70 and 80 using prime factorisation method.
Answer
LCM( 60, 70, 80 ) = 1680
Explanation
Step 1: Write down factorisation of each number:
60 = 2 · 2 · 3 · 5
70 = 2 · 5 · 7
80 = 2 · 2 · 2 · 2 · 5
Step 2 : Match primes vertically:
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||
| 70 | = | 2 | · | 5 | · | 7 | ||||||||
| 80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||
| 70 | = | 2 | · | 5 | · | 7 | ||||||||||
| 80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 1680 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
This page was created using
LCM Calculator