Least Common Multiple (LCM) of 84 and 129
The least common multiple (LCM) of 84 and 129 is 3612.
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 84 and 129?
First, calculate the GCD of 84 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 129 = 0 remainder 84 |
| 2 | 129 ÷ 84 = 1 remainder 45 |
| 3 | 84 ÷ 45 = 1 remainder 39 |
| 4 | 45 ÷ 39 = 1 remainder 6 |
| 5 | 39 ÷ 6 = 6 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 83 | 996 |
| 23 and 197 | 4531 |
| 186 and 123 | 7626 |
| 41 and 91 | 3731 |
| 43 and 178 | 7654 |