Least Common Multiple (LCM) of 199 and 113
The least common multiple (LCM) of 199 and 113 is 22487.
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 199 and 113?
First, calculate the GCD of 199 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 113 = 1 remainder 86 |
| 2 | 113 ÷ 86 = 1 remainder 27 |
| 3 | 86 ÷ 27 = 3 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 196 | 980 |
| 44 and 21 | 924 |
| 20 and 41 | 820 |
| 72 and 60 | 360 |
| 119 and 83 | 9877 |