Least Common Multiple (LCM) of 57 and 126
The least common multiple (LCM) of 57 and 126 is 2394.
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 126?
First, calculate the GCD of 57 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 126 = 0 remainder 57 |
| 2 | 126 ÷ 57 = 2 remainder 12 |
| 3 | 57 ÷ 12 = 4 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 168 | 2184 |
| 181 and 69 | 12489 |
| 126 and 182 | 1638 |
| 192 and 100 | 4800 |
| 125 and 142 | 17750 |