Least Common Multiple (LCM) of 129 and 74
The least common multiple (LCM) of 129 and 74 is 9546.
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 74?
First, calculate the GCD of 129 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 74 = 1 remainder 55 |
| 2 | 74 ÷ 55 = 1 remainder 19 |
| 3 | 55 ÷ 19 = 2 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 112 | 10416 |
| 18 and 83 | 1494 |
| 165 and 188 | 31020 |
| 106 and 16 | 848 |
| 194 and 87 | 16878 |