Least Common Multiple (LCM) of 159 and 189
The least common multiple (LCM) of 159 and 189 is 10017.
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 159 and 189?
First, calculate the GCD of 159 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 189 = 0 remainder 159 |
| 2 | 189 ÷ 159 = 1 remainder 30 |
| 3 | 159 ÷ 30 = 5 remainder 9 |
| 4 | 30 ÷ 9 = 3 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 38 | 1558 |
| 67 and 191 | 12797 |
| 155 and 82 | 12710 |
| 76 and 122 | 4636 |
| 199 and 125 | 24875 |