Find Least Common Multiple of 84, 120 and 210 using prime factorisation method.
Answer
LCM( 84, 120, 210 ) = 840
Explanation
Step 1: Write down factorisation of each number:
84 = 2 · 2 · 3 · 7
120 = 2 · 2 · 2 · 3 · 5
210 = 2 · 3 · 5 · 7
Step 2 : Match primes vertically:
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||
| 210 | = | 2 | · | 3 | · | 5 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||
| 210 | = | 2 | · | 3 | · | 5 | · | 7 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 840 |
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