Least Common Multiple (LCM) of 110 and 85
The least common multiple (LCM) of 110 and 85 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 110 and 85?
First, calculate the GCD of 110 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 85 = 1 remainder 25 |
| 2 | 85 ÷ 25 = 3 remainder 10 |
| 3 | 25 ÷ 10 = 2 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 126 | 3654 |
| 113 and 133 | 15029 |
| 82 and 87 | 7134 |
| 161 and 154 | 3542 |
| 187 and 159 | 29733 |