Least Common Multiple (LCM) of 120 and 129
The least common multiple (LCM) of 120 and 129 is 5160.
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 120 and 129?
First, calculate the GCD of 120 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 129 = 0 remainder 120 |
| 2 | 129 ÷ 120 = 1 remainder 9 |
| 3 | 120 ÷ 9 = 13 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 103 | 13802 |
| 92 and 128 | 2944 |
| 184 and 37 | 6808 |
| 105 and 133 | 1995 |
| 113 and 153 | 17289 |