Least Common Multiple (LCM) of 75 and 170
The least common multiple (LCM) of 75 and 170 is 2550.
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 75 and 170?
First, calculate the GCD of 75 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 170 = 0 remainder 75 |
| 2 | 170 ÷ 75 = 2 remainder 20 |
| 3 | 75 ÷ 20 = 3 remainder 15 |
| 4 | 20 ÷ 15 = 1 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 145 | 7105 |
| 20 and 76 | 380 |
| 199 and 177 | 35223 |
| 42 and 12 | 84 |
| 181 and 165 | 29865 |