Least Common Multiple (LCM) of 111 and 181
The least common multiple (LCM) of 111 and 181 is 20091.
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 181?
First, calculate the GCD of 111 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 181 = 0 remainder 111 |
| 2 | 181 ÷ 111 = 1 remainder 70 |
| 3 | 111 ÷ 70 = 1 remainder 41 |
| 4 | 70 ÷ 41 = 1 remainder 29 |
| 5 | 41 ÷ 29 = 1 remainder 12 |
| 6 | 29 ÷ 12 = 2 remainder 5 |
| 7 | 12 ÷ 5 = 2 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 181 | 18100 |
| 55 and 175 | 1925 |
| 63 and 60 | 1260 |
| 86 and 54 | 2322 |
| 70 and 164 | 5740 |