Least Common Multiple (LCM) of 189 and 85
The least common multiple (LCM) of 189 and 85 is 16065.
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 85?
First, calculate the GCD of 189 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 85 = 2 remainder 19 |
| 2 | 85 ÷ 19 = 4 remainder 9 |
| 3 | 19 ÷ 9 = 2 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 147 | 2793 |
| 33 and 35 | 1155 |
| 25 and 33 | 825 |
| 96 and 104 | 1248 |
| 100 and 143 | 14300 |