Least Common Multiple (LCM) of 197 and 108
The least common multiple (LCM) of 197 and 108 is 21276.
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 108?
First, calculate the GCD of 197 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 108 = 1 remainder 89 |
| 2 | 108 ÷ 89 = 1 remainder 19 |
| 3 | 89 ÷ 19 = 4 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 174 | 2610 |
| 75 and 11 | 825 |
| 182 and 135 | 24570 |
| 173 and 183 | 31659 |
| 109 and 111 | 12099 |