Least Common Multiple (LCM) of 57 and 109
The least common multiple (LCM) of 57 and 109 is 6213.
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 109?
First, calculate the GCD of 57 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 109 = 0 remainder 57 |
| 2 | 109 ÷ 57 = 1 remainder 52 |
| 3 | 57 ÷ 52 = 1 remainder 5 |
| 4 | 52 ÷ 5 = 10 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 178 | 12638 |
| 51 and 145 | 7395 |
| 116 and 143 | 16588 |
| 10 and 107 | 1070 |
| 195 and 105 | 1365 |