Least Common Multiple (LCM) of 113 and 191
The least common multiple (LCM) of 113 and 191 is 21583.
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 113 and 191?
First, calculate the GCD of 113 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 191 = 0 remainder 113 |
| 2 | 191 ÷ 113 = 1 remainder 78 |
| 3 | 113 ÷ 78 = 1 remainder 35 |
| 4 | 78 ÷ 35 = 2 remainder 8 |
| 5 | 35 ÷ 8 = 4 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 164 | 5412 |
| 186 and 65 | 12090 |
| 25 and 85 | 425 |
| 80 and 68 | 1360 |
| 41 and 53 | 2173 |