Least Common Multiple (LCM) of 189 and 111
The least common multiple (LCM) of 189 and 111 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 189 and 111?
First, calculate the GCD of 189 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 111 = 1 remainder 78 |
| 2 | 111 ÷ 78 = 1 remainder 33 |
| 3 | 78 ÷ 33 = 2 remainder 12 |
| 4 | 33 ÷ 12 = 2 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 189 | 10017 |
| 77 and 175 | 1925 |
| 185 and 53 | 9805 |
| 114 and 142 | 8094 |
| 107 and 61 | 6527 |