Least Common Multiple (LCM) of 129 and 76
The least common multiple (LCM) of 129 and 76 is 9804.
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 76?
First, calculate the GCD of 129 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 76 = 1 remainder 53 |
| 2 | 76 ÷ 53 = 1 remainder 23 |
| 3 | 53 ÷ 23 = 2 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 69 | 2829 |
| 173 and 190 | 32870 |
| 76 and 74 | 2812 |
| 64 and 38 | 1216 |
| 63 and 171 | 1197 |