Least Common Multiple (LCM) of 165 and 109
The least common multiple (LCM) of 165 and 109 is 17985.
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 109?
First, calculate the GCD of 165 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 109 = 1 remainder 56 |
| 2 | 109 ÷ 56 = 1 remainder 53 |
| 3 | 56 ÷ 53 = 1 remainder 3 |
| 4 | 53 ÷ 3 = 17 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 68 | 2108 |
| 51 and 127 | 6477 |
| 140 and 15 | 420 |
| 37 and 173 | 6401 |
| 173 and 181 | 31313 |