Least Common Multiple (LCM) of 103 and 115
The least common multiple (LCM) of 103 and 115 is 11845.
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 115?
First, calculate the GCD of 103 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 115 = 0 remainder 103 |
| 2 | 115 ÷ 103 = 1 remainder 12 |
| 3 | 103 ÷ 12 = 8 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 116 | 8004 |
| 100 and 102 | 5100 |
| 147 and 55 | 8085 |
| 53 and 200 | 10600 |
| 81 and 175 | 14175 |