Least Common Multiple (LCM) of 57 and 108
The least common multiple (LCM) of 57 and 108 is 2052.
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 108?
First, calculate the GCD of 57 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 108 = 0 remainder 57 |
| 2 | 108 ÷ 57 = 1 remainder 51 |
| 3 | 57 ÷ 51 = 1 remainder 6 |
| 4 | 51 ÷ 6 = 8 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 78 | 4368 |
| 71 and 96 | 6816 |
| 138 and 133 | 18354 |
| 48 and 126 | 1008 |
| 192 and 42 | 1344 |