Least Common Multiple (LCM) of 191 and 107
The least common multiple (LCM) of 191 and 107 is 20437.
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 107?
First, calculate the GCD of 191 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 107 = 1 remainder 84 |
| 2 | 107 ÷ 84 = 1 remainder 23 |
| 3 | 84 ÷ 23 = 3 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 102 | 4590 |
| 108 and 175 | 18900 |
| 146 and 26 | 1898 |
| 193 and 182 | 35126 |
| 61 and 129 | 7869 |