Least Common Multiple (LCM) of 109 and 197
The least common multiple (LCM) of 109 and 197 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 109 and 197?
First, calculate the GCD of 109 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 197 = 0 remainder 109 |
| 2 | 197 ÷ 109 = 1 remainder 88 |
| 3 | 109 ÷ 88 = 1 remainder 21 |
| 4 | 88 ÷ 21 = 4 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 38 | 1254 |
| 105 and 47 | 4935 |
| 115 and 70 | 1610 |
| 76 and 92 | 1748 |
| 12 and 81 | 324 |