Least Common Multiple (LCM) of 144 and 45
The least common multiple (LCM) of 144 and 45 is 720.
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 45?
First, calculate the GCD of 144 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 45 = 3 remainder 9 |
| 2 | 45 ÷ 9 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 198 | 3960 |
| 40 and 110 | 440 |
| 90 and 200 | 1800 |
| 175 and 92 | 16100 |
| 109 and 188 | 20492 |