Least Common Multiple (LCM) of 144 and 57
The least common multiple (LCM) of 144 and 57 is 2736.
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 57?
First, calculate the GCD of 144 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 57 = 2 remainder 30 |
| 2 | 57 ÷ 30 = 1 remainder 27 |
| 3 | 30 ÷ 27 = 1 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 26 | 1794 |
| 115 and 17 | 1955 |
| 193 and 67 | 12931 |
| 63 and 120 | 2520 |
| 122 and 69 | 8418 |