Least Common Multiple (LCM) of 38 and 57
The least common multiple (LCM) of 38 and 57 is 114.
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 38 and 57?
First, calculate the GCD of 38 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 57 = 0 remainder 38 |
| 2 | 57 ÷ 38 = 1 remainder 19 |
| 3 | 38 ÷ 19 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 106 | 7526 |
| 83 and 52 | 4316 |
| 175 and 44 | 7700 |
| 60 and 30 | 60 |
| 200 and 77 | 15400 |