Least Common Multiple (LCM) of 109 and 189
The least common multiple (LCM) of 109 and 189 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 109 and 189?
First, calculate the GCD of 109 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 189 = 0 remainder 109 |
| 2 | 189 ÷ 109 = 1 remainder 80 |
| 3 | 109 ÷ 80 = 1 remainder 29 |
| 4 | 80 ÷ 29 = 2 remainder 22 |
| 5 | 29 ÷ 22 = 1 remainder 7 |
| 6 | 22 ÷ 7 = 3 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 167 | 32064 |
| 83 and 68 | 5644 |
| 157 and 49 | 7693 |
| 183 and 182 | 33306 |
| 111 and 138 | 5106 |