Least Common Multiple (LCM) of 83 and 109
The least common multiple (LCM) of 83 and 109 is 9047.
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 83 and 109?
First, calculate the GCD of 83 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 109 = 0 remainder 83 |
| 2 | 109 ÷ 83 = 1 remainder 26 |
| 3 | 83 ÷ 26 = 3 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 188 | 31020 |
| 105 and 106 | 11130 |
| 98 and 71 | 6958 |
| 182 and 69 | 12558 |
| 105 and 83 | 8715 |