Least Common Multiple (LCM) of 115 and 175
The least common multiple (LCM) of 115 and 175 is 4025.
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 115 and 175?
First, calculate the GCD of 115 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 175 = 0 remainder 115 |
| 2 | 175 ÷ 115 = 1 remainder 60 |
| 3 | 115 ÷ 60 = 1 remainder 55 |
| 4 | 60 ÷ 55 = 1 remainder 5 |
| 5 | 55 ÷ 5 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 41 | 3075 |
| 78 and 28 | 1092 |
| 100 and 186 | 9300 |
| 163 and 59 | 9617 |
| 106 and 142 | 7526 |