Least Common Multiple (LCM) of 65 and 109
The least common multiple (LCM) of 65 and 109 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 65 and 109?
First, calculate the GCD of 65 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 109 = 0 remainder 65 |
| 2 | 109 ÷ 65 = 1 remainder 44 |
| 3 | 65 ÷ 44 = 1 remainder 21 |
| 4 | 44 ÷ 21 = 2 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 135 | 1350 |
| 22 and 136 | 1496 |
| 187 and 32 | 5984 |
| 106 and 54 | 2862 |
| 163 and 133 | 21679 |