Least Common Multiple (LCM) of 197 and 122
The least common multiple (LCM) of 197 and 122 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 197 and 122?
First, calculate the GCD of 197 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 122 = 1 remainder 75 |
| 2 | 122 ÷ 75 = 1 remainder 47 |
| 3 | 75 ÷ 47 = 1 remainder 28 |
| 4 | 47 ÷ 28 = 1 remainder 19 |
| 5 | 28 ÷ 19 = 1 remainder 9 |
| 6 | 19 ÷ 9 = 2 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 105 | 3570 |
| 77 and 101 | 7777 |
| 140 and 159 | 22260 |
| 72 and 16 | 144 |
| 188 and 69 | 12972 |