Least Common Multiple (LCM) of 57 and 112
The least common multiple (LCM) of 57 and 112 is 6384.
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 57 and 112?
First, calculate the GCD of 57 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 112 = 0 remainder 57 |
| 2 | 112 ÷ 57 = 1 remainder 55 |
| 3 | 57 ÷ 55 = 1 remainder 2 |
| 4 | 55 ÷ 2 = 27 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 153 | 9945 |
| 56 and 102 | 2856 |
| 173 and 13 | 2249 |
| 118 and 52 | 3068 |
| 118 and 10 | 590 |