Least Common Multiple (LCM) of 17 and 10
The least common multiple (LCM) of 17 and 10 is 170.
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 10?
First, calculate the GCD of 17 and 10 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 10 = 1 remainder 7 |
| 2 | 10 ÷ 7 = 1 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 106 | 20882 |
| 195 and 50 | 1950 |
| 75 and 175 | 525 |
| 157 and 195 | 30615 |
| 189 and 118 | 22302 |