Least Common Multiple (LCM) of 51 and 129
The least common multiple (LCM) of 51 and 129 is 2193.
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 51 and 129?
First, calculate the GCD of 51 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 129 = 0 remainder 51 |
| 2 | 129 ÷ 51 = 2 remainder 27 |
| 3 | 51 ÷ 27 = 1 remainder 24 |
| 4 | 27 ÷ 24 = 1 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 78 | 5460 |
| 133 and 194 | 25802 |
| 129 and 147 | 6321 |
| 19 and 178 | 3382 |
| 94 and 104 | 4888 |