Least Common Multiple (LCM) of 197 and 119
The least common multiple (LCM) of 197 and 119 is 23443.
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 197 and 119?
First, calculate the GCD of 197 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 119 = 1 remainder 78 |
| 2 | 119 ÷ 78 = 1 remainder 41 |
| 3 | 78 ÷ 41 = 1 remainder 37 |
| 4 | 41 ÷ 37 = 1 remainder 4 |
| 5 | 37 ÷ 4 = 9 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 65 | 7410 |
| 186 and 154 | 14322 |
| 186 and 109 | 20274 |
| 104 and 77 | 8008 |
| 84 and 145 | 12180 |