Least Common Multiple (LCM) of 129 and 160
The least common multiple (LCM) of 129 and 160 is 20640.
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 160?
First, calculate the GCD of 129 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 160 = 0 remainder 129 |
| 2 | 160 ÷ 129 = 1 remainder 31 |
| 3 | 129 ÷ 31 = 4 remainder 5 |
| 4 | 31 ÷ 5 = 6 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 40 | 680 |
| 32 and 38 | 608 |
| 174 and 107 | 18618 |
| 121 and 53 | 6413 |
| 86 and 49 | 4214 |