Least Common Multiple (LCM) of 144 and 159
The least common multiple (LCM) of 144 and 159 is 7632.
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 144 and 159?
First, calculate the GCD of 144 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 159 = 0 remainder 144 |
| 2 | 159 ÷ 144 = 1 remainder 15 |
| 3 | 144 ÷ 15 = 9 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 187 | 1122 |
| 118 and 175 | 20650 |
| 108 and 195 | 7020 |
| 75 and 171 | 4275 |
| 84 and 184 | 3864 |