Least Common Multiple (LCM) of 111 and 57
The least common multiple (LCM) of 111 and 57 is 2109.
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 111 and 57?
First, calculate the GCD of 111 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 57 = 1 remainder 54 |
| 2 | 57 ÷ 54 = 1 remainder 3 |
| 3 | 54 ÷ 3 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 125 | 7000 |
| 39 and 97 | 3783 |
| 140 and 188 | 6580 |
| 33 and 36 | 396 |
| 23 and 135 | 3105 |