Least Common Multiple (LCM) of 189 and 159
The least common multiple (LCM) of 189 and 159 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 189 and 159?
First, calculate the GCD of 189 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 159 = 1 remainder 30 |
| 2 | 159 ÷ 30 = 5 remainder 9 |
| 3 | 30 ÷ 9 = 3 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 82 | 1394 |
| 131 and 63 | 8253 |
| 108 and 144 | 432 |
| 56 and 133 | 1064 |
| 112 and 137 | 15344 |