Least Common Multiple (LCM) of 106 and 189
The least common multiple (LCM) of 106 and 189 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 106 and 189?
First, calculate the GCD of 106 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 189 = 0 remainder 106 |
| 2 | 189 ÷ 106 = 1 remainder 83 |
| 3 | 106 ÷ 83 = 1 remainder 23 |
| 4 | 83 ÷ 23 = 3 remainder 14 |
| 5 | 23 ÷ 14 = 1 remainder 9 |
| 6 | 14 ÷ 9 = 1 remainder 5 |
| 7 | 9 ÷ 5 = 1 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 45 | 5040 |
| 42 and 77 | 462 |
| 101 and 33 | 3333 |
| 165 and 53 | 8745 |
| 62 and 192 | 5952 |