Find Least Common Multiple of 24, 172 and 144 using prime factorisation method.
Answer
LCM( 24, 172, 144 ) = 6192
Explanation
Step 1: Write down factorisation of each number:
24 = 2 · 2 · 2 · 3
172 = 2 · 2 · 43
144 = 2 · 2 · 2 · 2 · 3 · 3
Step 2 : Match primes vertically:
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 172 | = | 2 | · | 2 | · | 43 | ||||||||
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 172 | = | 2 | · | 2 | · | 43 | ||||||||||
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 43 | = | 6192 |
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