Least Common Multiple (LCM) of 65 and 122
The least common multiple (LCM) of 65 and 122 is 7930.
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 65 and 122?
First, calculate the GCD of 65 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 122 = 0 remainder 65 |
| 2 | 122 ÷ 65 = 1 remainder 57 |
| 3 | 65 ÷ 57 = 1 remainder 8 |
| 4 | 57 ÷ 8 = 7 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 63 | 12600 |
| 109 and 109 | 109 |
| 59 and 134 | 7906 |
| 200 and 76 | 3800 |
| 177 and 81 | 4779 |