Least Common Multiple (LCM) of 144 and 40
The least common multiple (LCM) of 144 and 40 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 40?
First, calculate the GCD of 144 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 40 = 3 remainder 24 |
| 2 | 40 ÷ 24 = 1 remainder 16 |
| 3 | 24 ÷ 16 = 1 remainder 8 |
| 4 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 132 | 1980 |
| 74 and 68 | 2516 |
| 26 and 52 | 52 |
| 38 and 47 | 1786 |
| 180 and 161 | 28980 |