Least Common Multiple (LCM) of 109 and 57
The least common multiple (LCM) of 109 and 57 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 109 and 57?
First, calculate the GCD of 109 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 57 = 1 remainder 52 |
| 2 | 57 ÷ 52 = 1 remainder 5 |
| 3 | 52 ÷ 5 = 10 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 94 | 4512 |
| 175 and 59 | 10325 |
| 180 and 38 | 3420 |
| 42 and 178 | 3738 |
| 82 and 140 | 5740 |