Least Common Multiple (LCM) of 21 and 129
The least common multiple (LCM) of 21 and 129 is 903.
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 21 and 129?
First, calculate the GCD of 21 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 129 = 0 remainder 21 |
| 2 | 129 ÷ 21 = 6 remainder 3 |
| 3 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 186 | 11346 |
| 186 and 80 | 7440 |
| 141 and 200 | 28200 |
| 47 and 43 | 2021 |
| 140 and 72 | 2520 |