Least Common Multiple (LCM) of 189 and 105
The least common multiple (LCM) of 189 and 105 is 945.
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 105?
First, calculate the GCD of 189 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 105 = 1 remainder 84 |
| 2 | 105 ÷ 84 = 1 remainder 21 |
| 3 | 84 ÷ 21 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 126 | 1890 |
| 120 and 12 | 120 |
| 172 and 28 | 1204 |
| 23 and 181 | 4163 |
| 161 and 83 | 13363 |