Least Common Multiple (LCM) of 159 and 180
The least common multiple (LCM) of 159 and 180 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 159 and 180?
First, calculate the GCD of 159 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 180 = 0 remainder 159 |
| 2 | 180 ÷ 159 = 1 remainder 21 |
| 3 | 159 ÷ 21 = 7 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 75 | 6675 |
| 164 and 101 | 16564 |
| 109 and 188 | 20492 |
| 65 and 95 | 1235 |
| 166 and 76 | 6308 |