Least Common Multiple (LCM) of 191 and 119
The least common multiple (LCM) of 191 and 119 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 191 and 119?
First, calculate the GCD of 191 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 119 = 1 remainder 72 |
| 2 | 119 ÷ 72 = 1 remainder 47 |
| 3 | 72 ÷ 47 = 1 remainder 25 |
| 4 | 47 ÷ 25 = 1 remainder 22 |
| 5 | 25 ÷ 22 = 1 remainder 3 |
| 6 | 22 ÷ 3 = 7 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 66 | 6072 |
| 83 and 153 | 12699 |
| 175 and 22 | 3850 |
| 105 and 146 | 15330 |
| 71 and 117 | 8307 |