Least Common Multiple (LCM) of 144 and 165
The least common multiple (LCM) of 144 and 165 is 7920.
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 165?
First, calculate the GCD of 144 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 165 = 0 remainder 144 |
| 2 | 165 ÷ 144 = 1 remainder 21 |
| 3 | 144 ÷ 21 = 6 remainder 18 |
| 4 | 21 ÷ 18 = 1 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 129 | 12513 |
| 96 and 106 | 5088 |
| 110 and 34 | 1870 |
| 57 and 133 | 399 |
| 159 and 190 | 30210 |