Least Common Multiple (LCM) of 170 and 75
The least common multiple (LCM) of 170 and 75 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 170 and 75?
First, calculate the GCD of 170 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 75 = 2 remainder 20 |
| 2 | 75 ÷ 20 = 3 remainder 15 |
| 3 | 20 ÷ 15 = 1 remainder 5 |
| 4 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 177 | 7965 |
| 92 and 129 | 11868 |
| 111 and 166 | 18426 |
| 157 and 49 | 7693 |
| 117 and 175 | 20475 |