Least Common Multiple (LCM) of 103 and 57
The least common multiple (LCM) of 103 and 57 is 5871.
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 103 and 57?
First, calculate the GCD of 103 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 57 = 1 remainder 46 |
| 2 | 57 ÷ 46 = 1 remainder 11 |
| 3 | 46 ÷ 11 = 4 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 123 | 1845 |
| 80 and 81 | 6480 |
| 144 and 100 | 3600 |
| 102 and 98 | 4998 |
| 52 and 154 | 4004 |