Least Common Multiple (LCM) of 129 and 105
The least common multiple (LCM) of 129 and 105 is 4515.
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 105?
First, calculate the GCD of 129 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 105 = 1 remainder 24 |
| 2 | 105 ÷ 24 = 4 remainder 9 |
| 3 | 24 ÷ 9 = 2 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 54 | 7830 |
| 49 and 195 | 9555 |
| 153 and 99 | 1683 |
| 118 and 106 | 6254 |
| 164 and 115 | 18860 |