Least Common Multiple (LCM) of 192 and 57
The least common multiple (LCM) of 192 and 57 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 192 and 57?
First, calculate the GCD of 192 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 57 = 3 remainder 21 |
| 2 | 57 ÷ 21 = 2 remainder 15 |
| 3 | 21 ÷ 15 = 1 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 192 | 1344 |
| 166 and 156 | 12948 |
| 177 and 116 | 20532 |
| 120 and 148 | 4440 |
| 11 and 15 | 165 |