Least Common Multiple (LCM) of 17 and 175
The least common multiple (LCM) of 17 and 175 is 2975.
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 17 and 175?
First, calculate the GCD of 17 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 175 = 0 remainder 17 |
| 2 | 175 ÷ 17 = 10 remainder 5 |
| 3 | 17 ÷ 5 = 3 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 165 | 10560 |
| 187 and 10 | 1870 |
| 66 and 69 | 1518 |
| 24 and 21 | 168 |
| 189 and 148 | 27972 |