Least Common Multiple (LCM) of 180 and 159
The least common multiple (LCM) of 180 and 159 is 9540.
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 180 and 159?
First, calculate the GCD of 180 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 159 = 1 remainder 21 |
| 2 | 159 ÷ 21 = 7 remainder 12 |
| 3 | 21 ÷ 12 = 1 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 105 | 5565 |
| 147 and 144 | 7056 |
| 166 and 176 | 14608 |
| 189 and 18 | 378 |
| 22 and 110 | 110 |