Least Common Multiple (LCM) of 156 and 129
The least common multiple (LCM) of 156 and 129 is 6708.
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 156 and 129?
First, calculate the GCD of 156 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 129 = 1 remainder 27 |
| 2 | 129 ÷ 27 = 4 remainder 21 |
| 3 | 27 ÷ 21 = 1 remainder 6 |
| 4 | 21 ÷ 6 = 3 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 112 | 336 |
| 95 and 20 | 380 |
| 148 and 36 | 1332 |
| 142 and 196 | 13916 |
| 43 and 33 | 1419 |