Least Common Multiple (LCM) of 66 and 85
The least common multiple (LCM) of 66 and 85 is 5610.
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 66 and 85?
First, calculate the GCD of 66 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 85 = 0 remainder 66 |
| 2 | 85 ÷ 66 = 1 remainder 19 |
| 3 | 66 ÷ 19 = 3 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 65 | 2080 |
| 140 and 200 | 1400 |
| 123 and 166 | 20418 |
| 160 and 180 | 1440 |
| 16 and 55 | 880 |