Least Common Multiple (LCM) of 113 and 199
The least common multiple (LCM) of 113 and 199 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 113 and 199?
First, calculate the GCD of 113 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 199 = 0 remainder 113 |
| 2 | 199 ÷ 113 = 1 remainder 86 |
| 3 | 113 ÷ 86 = 1 remainder 27 |
| 4 | 86 ÷ 27 = 3 remainder 5 |
| 5 | 27 ÷ 5 = 5 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 89 | 1335 |
| 165 and 109 | 17985 |
| 160 and 30 | 480 |
| 41 and 38 | 1558 |
| 31 and 189 | 5859 |