Least Common Multiple (LCM) of 58 and 199
The least common multiple (LCM) of 58 and 199 is 11542.
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 58 and 199?
First, calculate the GCD of 58 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 199 = 0 remainder 58 |
| 2 | 199 ÷ 58 = 3 remainder 25 |
| 3 | 58 ÷ 25 = 2 remainder 8 |
| 4 | 25 ÷ 8 = 3 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 165 | 24915 |
| 25 and 163 | 4075 |
| 58 and 109 | 6322 |
| 41 and 176 | 7216 |
| 170 and 109 | 18530 |