Least Common Multiple (LCM) of 189 and 109
The least common multiple (LCM) of 189 and 109 is 20601.
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 109?
First, calculate the GCD of 189 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 109 = 1 remainder 80 |
| 2 | 109 ÷ 80 = 1 remainder 29 |
| 3 | 80 ÷ 29 = 2 remainder 22 |
| 4 | 29 ÷ 22 = 1 remainder 7 |
| 5 | 22 ÷ 7 = 3 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 58 | 2726 |
| 195 and 172 | 33540 |
| 88 and 143 | 1144 |
| 38 and 153 | 5814 |
| 137 and 106 | 14522 |