Least Common Multiple (LCM) of 59 and 115
The least common multiple (LCM) of 59 and 115 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 59 and 115?
First, calculate the GCD of 59 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 115 = 0 remainder 59 |
| 2 | 115 ÷ 59 = 1 remainder 56 |
| 3 | 59 ÷ 56 = 1 remainder 3 |
| 4 | 56 ÷ 3 = 18 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 83 | 2739 |
| 197 and 100 | 19700 |
| 154 and 59 | 9086 |
| 116 and 88 | 2552 |
| 23 and 185 | 4255 |