Least Common Multiple (LCM) of 97 and 57
The least common multiple (LCM) of 97 and 57 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 97 and 57?
First, calculate the GCD of 97 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 57 = 1 remainder 40 |
| 2 | 57 ÷ 40 = 1 remainder 17 |
| 3 | 40 ÷ 17 = 2 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 |
|---|---|
| 20 and 165 | 660 |
| 198 and 48 | 1584 |
| 138 and 184 | 552 |
| 86 and 130 | 5590 |
| 56 and 176 | 1232 |