Least Common Multiple (LCM) of 57 and 191
The least common multiple (LCM) of 57 and 191 is 10887.
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 191?
First, calculate the GCD of 57 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 191 = 0 remainder 57 |
| 2 | 191 ÷ 57 = 3 remainder 20 |
| 3 | 57 ÷ 20 = 2 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 88 | 9944 |
| 59 and 29 | 1711 |
| 99 and 122 | 12078 |
| 77 and 109 | 8393 |
| 128 and 59 | 7552 |