Least Common Multiple (LCM) of 57 and 192
The least common multiple (LCM) of 57 and 192 is 3648.
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 192?
First, calculate the GCD of 57 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 192 = 0 remainder 57 |
| 2 | 192 ÷ 57 = 3 remainder 21 |
| 3 | 57 ÷ 21 = 2 remainder 15 |
| 4 | 21 ÷ 15 = 1 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 12 | 156 |
| 170 and 97 | 16490 |
| 15 and 87 | 435 |
| 194 and 120 | 11640 |
| 60 and 60 | 60 |