Least Common Multiple (LCM) of 58 and 113
The least common multiple (LCM) of 58 and 113 is 6554.
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 113?
First, calculate the GCD of 58 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 113 = 0 remainder 58 |
| 2 | 113 ÷ 58 = 1 remainder 55 |
| 3 | 58 ÷ 55 = 1 remainder 3 |
| 4 | 55 ÷ 3 = 18 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 103 | 20291 |
| 135 and 118 | 15930 |
| 67 and 194 | 12998 |
| 111 and 19 | 2109 |
| 144 and 103 | 14832 |