Least Common Multiple (LCM) of 165 and 129
The least common multiple (LCM) of 165 and 129 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 165 and 129?
First, calculate the GCD of 165 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 129 = 1 remainder 36 |
| 2 | 129 ÷ 36 = 3 remainder 21 |
| 3 | 36 ÷ 21 = 1 remainder 15 |
| 4 | 21 ÷ 15 = 1 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 116 | 3132 |
| 15 and 141 | 705 |
| 69 and 72 | 1656 |
| 160 and 175 | 5600 |
| 152 and 54 | 4104 |