Least Common Multiple (LCM) of 85 and 110
The least common multiple (LCM) of 85 and 110 is 1870.
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 110?
First, calculate the GCD of 85 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 110 = 0 remainder 85 |
| 2 | 110 ÷ 85 = 1 remainder 25 |
| 3 | 85 ÷ 25 = 3 remainder 10 |
| 4 | 25 ÷ 10 = 2 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 20 | 820 |
| 85 and 108 | 9180 |
| 81 and 106 | 8586 |
| 135 and 24 | 1080 |
| 138 and 50 | 3450 |