Least Common Multiple (LCM) of 122 and 197
The least common multiple (LCM) of 122 and 197 is 24034.
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 122 and 197?
First, calculate the GCD of 122 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 197 = 0 remainder 122 |
| 2 | 197 ÷ 122 = 1 remainder 75 |
| 3 | 122 ÷ 75 = 1 remainder 47 |
| 4 | 75 ÷ 47 = 1 remainder 28 |
| 5 | 47 ÷ 28 = 1 remainder 19 |
| 6 | 28 ÷ 19 = 1 remainder 9 |
| 7 | 19 ÷ 9 = 2 remainder 1 |
| 8 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 32 | 224 |
| 99 and 102 | 3366 |
| 87 and 38 | 3306 |
| 160 and 44 | 1760 |
| 189 and 104 | 19656 |