Least Common Multiple (LCM) of 97 and 129
The least common multiple (LCM) of 97 and 129 is 12513.
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 97 and 129?
First, calculate the GCD of 97 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 129 = 0 remainder 97 |
| 2 | 129 ÷ 97 = 1 remainder 32 |
| 3 | 97 ÷ 32 = 3 remainder 1 |
| 4 | 32 ÷ 1 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 189 | 31563 |
| 146 and 104 | 7592 |
| 104 and 46 | 2392 |
| 17 and 20 | 340 |
| 128 and 107 | 13696 |