Least Common Multiple (LCM) of 67 and 129
The least common multiple (LCM) of 67 and 129 is 8643.
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 67 and 129?
First, calculate the GCD of 67 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 129 = 0 remainder 67 |
| 2 | 129 ÷ 67 = 1 remainder 62 |
| 3 | 67 ÷ 62 = 1 remainder 5 |
| 4 | 62 ÷ 5 = 12 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 10 | 1230 |
| 122 and 101 | 12322 |
| 145 and 198 | 28710 |
| 16 and 63 | 1008 |
| 172 and 185 | 31820 |