Least Common Multiple (LCM) of 76 and 129
The least common multiple (LCM) of 76 and 129 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 76 and 129?
First, calculate the GCD of 76 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 129 = 0 remainder 76 |
| 2 | 129 ÷ 76 = 1 remainder 53 |
| 3 | 76 ÷ 53 = 1 remainder 23 |
| 4 | 53 ÷ 23 = 2 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 34 | 3400 |
| 57 and 70 | 3990 |
| 178 and 120 | 10680 |
| 50 and 123 | 6150 |
| 131 and 190 | 24890 |