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 |
|---|---|
| 169 and 10 | 1690 |
| 189 and 118 | 22302 |
| 102 and 196 | 9996 |
| 157 and 93 | 14601 |
| 152 and 83 | 12616 |