Least Common Multiple (LCM) of 103 and 175
The least common multiple (LCM) of 103 and 175 is 18025.
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 175?
First, calculate the GCD of 103 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 175 = 0 remainder 103 |
| 2 | 175 ÷ 103 = 1 remainder 72 |
| 3 | 103 ÷ 72 = 1 remainder 31 |
| 4 | 72 ÷ 31 = 2 remainder 10 |
| 5 | 31 ÷ 10 = 3 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 28 | 2100 |
| 111 and 147 | 5439 |
| 177 and 184 | 32568 |
| 185 and 61 | 11285 |
| 126 and 175 | 3150 |