Least Common Multiple (LCM) of 102 and 144
The least common multiple (LCM) of 102 and 144 is 2448.
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 102 and 144?
First, calculate the GCD of 102 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 144 = 0 remainder 102 |
| 2 | 144 ÷ 102 = 1 remainder 42 |
| 3 | 102 ÷ 42 = 2 remainder 18 |
| 4 | 42 ÷ 18 = 2 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 108 | 20196 |
| 30 and 177 | 1770 |
| 31 and 65 | 2015 |
| 65 and 153 | 9945 |
| 133 and 82 | 10906 |