Least Common Multiple (LCM) of 104 and 57
The least common multiple (LCM) of 104 and 57 is 5928.
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 104 and 57?
First, calculate the GCD of 104 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 57 = 1 remainder 47 |
| 2 | 57 ÷ 47 = 1 remainder 10 |
| 3 | 47 ÷ 10 = 4 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 128 | 3968 |
| 67 and 76 | 5092 |
| 89 and 197 | 17533 |
| 68 and 128 | 2176 |
| 90 and 188 | 8460 |