Least Common Multiple (LCM) of 83 and 122
The least common multiple (LCM) of 83 and 122 is 10126.
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 83 and 122?
First, calculate the GCD of 83 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 122 = 0 remainder 83 |
| 2 | 122 ÷ 83 = 1 remainder 39 |
| 3 | 83 ÷ 39 = 2 remainder 5 |
| 4 | 39 ÷ 5 = 7 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 174 | 8526 |
| 133 and 173 | 23009 |
| 13 and 122 | 1586 |
| 109 and 175 | 19075 |
| 152 and 102 | 7752 |