Least Common Multiple (LCM) of 57 and 107
The least common multiple (LCM) of 57 and 107 is 6099.
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 107?
First, calculate the GCD of 57 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 107 = 0 remainder 57 |
| 2 | 107 ÷ 57 = 1 remainder 50 |
| 3 | 57 ÷ 50 = 1 remainder 7 |
| 4 | 50 ÷ 7 = 7 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 82 | 7462 |
| 155 and 140 | 4340 |
| 90 and 32 | 1440 |
| 102 and 50 | 2550 |
| 54 and 153 | 918 |