Least Common Multiple (LCM) of 111 and 197
The least common multiple (LCM) of 111 and 197 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 111 and 197?
First, calculate the GCD of 111 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 197 = 0 remainder 111 |
| 2 | 197 ÷ 111 = 1 remainder 86 |
| 3 | 111 ÷ 86 = 1 remainder 25 |
| 4 | 86 ÷ 25 = 3 remainder 11 |
| 5 | 25 ÷ 11 = 2 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 185 | 22385 |
| 172 and 172 | 172 |
| 164 and 53 | 8692 |
| 64 and 165 | 10560 |
| 178 and 107 | 19046 |