Least Common Multiple (LCM) of 57 and 188
The least common multiple (LCM) of 57 and 188 is 10716.
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 188?
First, calculate the GCD of 57 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 188 = 0 remainder 57 |
| 2 | 188 ÷ 57 = 3 remainder 17 |
| 3 | 57 ÷ 17 = 3 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 112 | 6384 |
| 52 and 97 | 5044 |
| 66 and 28 | 924 |
| 158 and 187 | 29546 |
| 188 and 42 | 3948 |