Least Common Multiple (LCM) of 67 and 57
The least common multiple (LCM) of 67 and 57 is 3819.
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 67 and 57?
First, calculate the GCD of 67 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 57 = 1 remainder 10 |
| 2 | 57 ÷ 10 = 5 remainder 7 |
| 3 | 10 ÷ 7 = 1 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 198 | 39006 |
| 13 and 107 | 1391 |
| 35 and 177 | 6195 |
| 179 and 28 | 5012 |
| 57 and 84 | 1596 |