Least Common Multiple (LCM) of 107 and 189
The least common multiple (LCM) of 107 and 189 is 20223.
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 107 and 189?
First, calculate the GCD of 107 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 189 = 0 remainder 107 |
| 2 | 189 ÷ 107 = 1 remainder 82 |
| 3 | 107 ÷ 82 = 1 remainder 25 |
| 4 | 82 ÷ 25 = 3 remainder 7 |
| 5 | 25 ÷ 7 = 3 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 57 | 570 |
| 159 and 172 | 27348 |
| 100 and 51 | 5100 |
| 94 and 141 | 282 |
| 128 and 75 | 9600 |