Least Common Multiple (LCM) of 85 and 122
The least common multiple (LCM) of 85 and 122 is 10370.
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 122?
First, calculate the GCD of 85 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 122 = 0 remainder 85 |
| 2 | 122 ÷ 85 = 1 remainder 37 |
| 3 | 85 ÷ 37 = 2 remainder 11 |
| 4 | 37 ÷ 11 = 3 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 63 | 1260 |
| 12 and 10 | 60 |
| 89 and 96 | 8544 |
| 144 and 174 | 4176 |
| 67 and 123 | 8241 |