Least Common Multiple (LCM) of 109 and 65
The least common multiple (LCM) of 109 and 65 is 7085.
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 109 and 65?
First, calculate the GCD of 109 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 65 = 1 remainder 44 |
| 2 | 65 ÷ 44 = 1 remainder 21 |
| 3 | 44 ÷ 21 = 2 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 80 | 1680 |
| 65 and 100 | 1300 |
| 55 and 23 | 1265 |
| 120 and 20 | 120 |
| 170 and 64 | 5440 |