Least Common Multiple (LCM) of 85 and 115
The least common multiple (LCM) of 85 and 115 is 1955.
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 85 and 115?
First, calculate the GCD of 85 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 115 = 0 remainder 85 |
| 2 | 115 ÷ 85 = 1 remainder 30 |
| 3 | 85 ÷ 30 = 2 remainder 25 |
| 4 | 30 ÷ 25 = 1 remainder 5 |
| 5 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 10 | 270 |
| 91 and 65 | 455 |
| 11 and 142 | 1562 |
| 37 and 38 | 1406 |
| 123 and 49 | 6027 |