Least Common Multiple (LCM) of 72 and 129
The least common multiple (LCM) of 72 and 129 is 3096.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 72 and 129?
First, calculate the GCD of 72 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 129 = 0 remainder 72 |
| 2 | 129 ÷ 72 = 1 remainder 57 |
| 3 | 72 ÷ 57 = 1 remainder 15 |
| 4 | 57 ÷ 15 = 3 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 141 | 3243 |
| 146 and 68 | 4964 |
| 72 and 184 | 1656 |
| 76 and 51 | 3876 |
| 172 and 52 | 2236 |