Least Common Multiple (LCM) of 129 and 85
The least common multiple (LCM) of 129 and 85 is 10965.
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 85?
First, calculate the GCD of 129 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 85 = 1 remainder 44 |
| 2 | 85 ÷ 44 = 1 remainder 41 |
| 3 | 44 ÷ 41 = 1 remainder 3 |
| 4 | 41 ÷ 3 = 13 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 188 | 36284 |
| 192 and 47 | 9024 |
| 90 and 143 | 12870 |
| 129 and 137 | 17673 |
| 31 and 158 | 4898 |