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 |
|---|---|
| 115 and 48 | 5520 |
| 193 and 176 | 33968 |
| 21 and 178 | 3738 |
| 99 and 121 | 1089 |
| 52 and 72 | 936 |