Least Common Multiple (LCM) of 129 and 167
The least common multiple (LCM) of 129 and 167 is 21543.
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 129 and 167?
First, calculate the GCD of 129 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 167 = 0 remainder 129 |
| 2 | 167 ÷ 129 = 1 remainder 38 |
| 3 | 129 ÷ 38 = 3 remainder 15 |
| 4 | 38 ÷ 15 = 2 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 177 | 1416 |
| 18 and 64 | 576 |
| 115 and 30 | 690 |
| 111 and 189 | 6993 |
| 47 and 81 | 3807 |