Least Common Multiple (LCM) of 197 and 109
The least common multiple (LCM) of 197 and 109 is 21473.
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 109?
First, calculate the GCD of 197 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 109 = 1 remainder 88 |
| 2 | 109 ÷ 88 = 1 remainder 21 |
| 3 | 88 ÷ 21 = 4 remainder 4 |
| 4 | 21 ÷ 4 = 5 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 194 | 12610 |
| 180 and 14 | 1260 |
| 113 and 31 | 3503 |
| 162 and 157 | 25434 |
| 77 and 143 | 1001 |