Least Common Multiple (LCM) of 107 and 109
The least common multiple (LCM) of 107 and 109 is 11663.
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 107 and 109?
First, calculate the GCD of 107 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 109 = 0 remainder 107 |
| 2 | 109 ÷ 107 = 1 remainder 2 |
| 3 | 107 ÷ 2 = 53 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 126 | 8442 |
| 109 and 170 | 18530 |
| 182 and 82 | 7462 |
| 189 and 45 | 945 |
| 128 and 153 | 19584 |