Least Common Multiple (LCM) of 109 and 83
The least common multiple (LCM) of 109 and 83 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 109 and 83?
First, calculate the GCD of 109 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 83 = 1 remainder 26 |
| 2 | 83 ÷ 26 = 3 remainder 5 |
| 3 | 26 ÷ 5 = 5 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 144 | 4464 |
| 192 and 49 | 9408 |
| 140 and 51 | 7140 |
| 173 and 154 | 26642 |
| 128 and 82 | 5248 |