Least Common Multiple (LCM) of 129 and 165
The least common multiple (LCM) of 129 and 165 is 7095.
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 165?
First, calculate the GCD of 129 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 165 = 0 remainder 129 |
| 2 | 165 ÷ 129 = 1 remainder 36 |
| 3 | 129 ÷ 36 = 3 remainder 21 |
| 4 | 36 ÷ 21 = 1 remainder 15 |
| 5 | 21 ÷ 15 = 1 remainder 6 |
| 6 | 15 ÷ 6 = 2 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 45 | 3420 |
| 18 and 102 | 306 |
| 70 and 58 | 2030 |
| 154 and 62 | 4774 |
| 76 and 188 | 3572 |