Least Common Multiple (LCM) of 111 and 189
The least common multiple (LCM) of 111 and 189 is 6993.
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 189?
First, calculate the GCD of 111 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 189 = 0 remainder 111 |
| 2 | 189 ÷ 111 = 1 remainder 78 |
| 3 | 111 ÷ 78 = 1 remainder 33 |
| 4 | 78 ÷ 33 = 2 remainder 12 |
| 5 | 33 ÷ 12 = 2 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 33 | 99 |
| 99 and 128 | 12672 |
| 21 and 159 | 1113 |
| 127 and 121 | 15367 |
| 134 and 57 | 7638 |