Least Common Multiple (LCM) of 197 and 111
The least common multiple (LCM) of 197 and 111 is 21867.
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 111?
First, calculate the GCD of 197 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 111 = 1 remainder 86 |
| 2 | 111 ÷ 86 = 1 remainder 25 |
| 3 | 86 ÷ 25 = 3 remainder 11 |
| 4 | 25 ÷ 11 = 2 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 36 | 1044 |
| 107 and 174 | 18618 |
| 112 and 138 | 7728 |
| 46 and 39 | 1794 |
| 52 and 119 | 6188 |