Least Common Multiple (LCM) of 103 and 59
The least common multiple (LCM) of 103 and 59 is 6077.
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 59?
First, calculate the GCD of 103 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 59 = 1 remainder 44 |
| 2 | 59 ÷ 44 = 1 remainder 15 |
| 3 | 44 ÷ 15 = 2 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 127 | 9779 |
| 188 and 91 | 17108 |
| 177 and 113 | 20001 |
| 125 and 193 | 24125 |
| 51 and 39 | 663 |