Least Common Multiple (LCM) of 119 and 191
The least common multiple (LCM) of 119 and 191 is 22729.
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 191?
First, calculate the GCD of 119 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 191 = 0 remainder 119 |
| 2 | 191 ÷ 119 = 1 remainder 72 |
| 3 | 119 ÷ 72 = 1 remainder 47 |
| 4 | 72 ÷ 47 = 1 remainder 25 |
| 5 | 47 ÷ 25 = 1 remainder 22 |
| 6 | 25 ÷ 22 = 1 remainder 3 |
| 7 | 22 ÷ 3 = 7 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 107 | 6741 |
| 49 and 83 | 4067 |
| 189 and 98 | 2646 |
| 198 and 108 | 1188 |
| 77 and 78 | 6006 |