Least Common Multiple (LCM) of 45 and 144
The least common multiple (LCM) of 45 and 144 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 45 and 144?
First, calculate the GCD of 45 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 144 = 0 remainder 45 |
| 2 | 144 ÷ 45 = 3 remainder 9 |
| 3 | 45 ÷ 9 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 127 | 9652 |
| 72 and 135 | 1080 |
| 130 and 186 | 12090 |
| 96 and 104 | 1248 |
| 142 and 47 | 6674 |