Least Common Multiple (LCM) of 189 and 106
The least common multiple (LCM) of 189 and 106 is 20034.
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 106?
First, calculate the GCD of 189 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 106 = 1 remainder 83 |
| 2 | 106 ÷ 83 = 1 remainder 23 |
| 3 | 83 ÷ 23 = 3 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 49 | 6223 |
| 54 and 56 | 1512 |
| 23 and 60 | 1380 |
| 193 and 37 | 7141 |
| 180 and 86 | 7740 |