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 |
|---|---|
| 182 and 148 | 13468 |
| 121 and 187 | 2057 |
| 10 and 49 | 490 |
| 29 and 41 | 1189 |
| 160 and 182 | 14560 |