Least Common Multiple (LCM) of 107 and 191
The least common multiple (LCM) of 107 and 191 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 107 and 191?
First, calculate the GCD of 107 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 191 = 0 remainder 107 |
| 2 | 191 ÷ 107 = 1 remainder 84 |
| 3 | 107 ÷ 84 = 1 remainder 23 |
| 4 | 84 ÷ 23 = 3 remainder 15 |
| 5 | 23 ÷ 15 = 1 remainder 8 |
| 6 | 15 ÷ 8 = 1 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 33 | 957 |
| 192 and 56 | 1344 |
| 183 and 53 | 9699 |
| 115 and 82 | 9430 |
| 89 and 117 | 10413 |