Least Common Multiple (LCM) of 57 and 97
The least common multiple (LCM) of 57 and 97 is 5529.
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 97?
First, calculate the GCD of 57 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 97 = 0 remainder 57 |
| 2 | 97 ÷ 57 = 1 remainder 40 |
| 3 | 57 ÷ 40 = 1 remainder 17 |
| 4 | 40 ÷ 17 = 2 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 82 | 13038 |
| 51 and 45 | 765 |
| 77 and 111 | 8547 |
| 42 and 125 | 5250 |
| 181 and 98 | 17738 |