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 |
|---|---|
| 56 and 33 | 1848 |
| 135 and 151 | 20385 |
| 173 and 85 | 14705 |
| 124 and 129 | 15996 |
| 140 and 81 | 11340 |