Least Common Multiple (LCM) of 114 and 85
The least common multiple (LCM) of 114 and 85 is 9690.
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 114 and 85?
First, calculate the GCD of 114 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 85 = 1 remainder 29 |
| 2 | 85 ÷ 29 = 2 remainder 27 |
| 3 | 29 ÷ 27 = 1 remainder 2 |
| 4 | 27 ÷ 2 = 13 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 26 | 2990 |
| 161 and 145 | 23345 |
| 200 and 133 | 26600 |
| 46 and 118 | 2714 |
| 60 and 104 | 1560 |