Least Common Multiple (LCM) of 129 and 63
The least common multiple (LCM) of 129 and 63 is 2709.
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 63?
First, calculate the GCD of 129 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 63 = 2 remainder 3 |
| 2 | 63 ÷ 3 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 23 | 2898 |
| 82 and 132 | 5412 |
| 101 and 103 | 10403 |
| 72 and 21 | 504 |
| 50 and 164 | 4100 |