Least Common Multiple (LCM) of 113 and 58
The least common multiple (LCM) of 113 and 58 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 113 and 58?
First, calculate the GCD of 113 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 58 = 1 remainder 55 |
| 2 | 58 ÷ 55 = 1 remainder 3 |
| 3 | 55 ÷ 3 = 18 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 106 | 3392 |
| 111 and 40 | 4440 |
| 65 and 87 | 5655 |
| 119 and 144 | 17136 |
| 125 and 135 | 3375 |