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 |
|---|---|
| 134 and 30 | 2010 |
| 106 and 21 | 2226 |
| 116 and 24 | 696 |
| 44 and 195 | 8580 |
| 112 and 157 | 17584 |