Least Common Multiple (LCM) of 189 and 107
The least common multiple (LCM) of 189 and 107 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 189 and 107?
First, calculate the GCD of 189 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 107 = 1 remainder 82 |
| 2 | 107 ÷ 82 = 1 remainder 25 |
| 3 | 82 ÷ 25 = 3 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 155 | 155 |
| 123 and 65 | 7995 |
| 37 and 176 | 6512 |
| 77 and 22 | 154 |
| 35 and 146 | 5110 |