Least Common Multiple (LCM) of 144 and 195
The least common multiple (LCM) of 144 and 195 is 9360.
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 195?
First, calculate the GCD of 144 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 195 = 0 remainder 144 |
| 2 | 195 ÷ 144 = 1 remainder 51 |
| 3 | 144 ÷ 51 = 2 remainder 42 |
| 4 | 51 ÷ 42 = 1 remainder 9 |
| 5 | 42 ÷ 9 = 4 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 35 | 2135 |
| 144 and 150 | 3600 |
| 78 and 141 | 3666 |
| 82 and 119 | 9758 |
| 42 and 85 | 3570 |