Least Common Multiple (LCM) of 159 and 192
The least common multiple (LCM) of 159 and 192 is 10176.
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 192?
First, calculate the GCD of 159 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 192 = 0 remainder 159 |
| 2 | 192 ÷ 159 = 1 remainder 33 |
| 3 | 159 ÷ 33 = 4 remainder 27 |
| 4 | 33 ÷ 27 = 1 remainder 6 |
| 5 | 27 ÷ 6 = 4 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 80 | 720 |
| 107 and 195 | 20865 |
| 48 and 156 | 624 |
| 96 and 89 | 8544 |
| 90 and 87 | 2610 |