Least Common Multiple (LCM) of 165 and 69
The least common multiple (LCM) of 165 and 69 is 3795.
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 69?
First, calculate the GCD of 165 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 69 = 2 remainder 27 |
| 2 | 69 ÷ 27 = 2 remainder 15 |
| 3 | 27 ÷ 15 = 1 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 131 | 6419 |
| 199 and 95 | 18905 |
| 193 and 97 | 18721 |
| 182 and 145 | 26390 |
| 108 and 138 | 2484 |