Least Common Multiple (LCM) of 115 and 59
The least common multiple (LCM) of 115 and 59 is 6785.
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 115 and 59?
First, calculate the GCD of 115 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 59 = 1 remainder 56 |
| 2 | 59 ÷ 56 = 1 remainder 3 |
| 3 | 56 ÷ 3 = 18 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 132 | 22044 |
| 40 and 75 | 600 |
| 32 and 158 | 2528 |
| 39 and 65 | 195 |
| 29 and 39 | 1131 |