Least Common Multiple (LCM) of 119 and 82
The least common multiple (LCM) of 119 and 82 is 9758.
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 82?
First, calculate the GCD of 119 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 82 = 1 remainder 37 |
| 2 | 82 ÷ 37 = 2 remainder 8 |
| 3 | 37 ÷ 8 = 4 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 40 | 6760 |
| 164 and 84 | 3444 |
| 18 and 20 | 180 |
| 25 and 22 | 550 |
| 122 and 137 | 16714 |