Least Common Multiple (LCM) of 83 and 119
The least common multiple (LCM) of 83 and 119 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 83 and 119?
First, calculate the GCD of 83 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 119 = 0 remainder 83 |
| 2 | 119 ÷ 83 = 1 remainder 36 |
| 3 | 83 ÷ 36 = 2 remainder 11 |
| 4 | 36 ÷ 11 = 3 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 11 | 902 |
| 45 and 47 | 2115 |
| 169 and 109 | 18421 |
| 181 and 65 | 11765 |
| 45 and 66 | 990 |