Least Common Multiple (LCM) of 17 and 57
The least common multiple (LCM) of 17 and 57 is 969.
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 17 and 57?
First, calculate the GCD of 17 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 57 = 0 remainder 17 |
| 2 | 57 ÷ 17 = 3 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 20 | 1620 |
| 197 and 37 | 7289 |
| 95 and 172 | 16340 |
| 152 and 82 | 6232 |
| 156 and 165 | 8580 |