Least Common Multiple (LCM) of 119 and 83
The least common multiple (LCM) of 119 and 83 is 9877.
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 119 and 83?
First, calculate the GCD of 119 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 83 = 1 remainder 36 |
| 2 | 83 ÷ 36 = 2 remainder 11 |
| 3 | 36 ÷ 11 = 3 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 168 | 1848 |
| 198 and 20 | 1980 |
| 191 and 103 | 19673 |
| 112 and 159 | 17808 |
| 86 and 86 | 86 |