Least Common Multiple (LCM) of 170 and 118
The least common multiple (LCM) of 170 and 118 is 10030.
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 118?
First, calculate the GCD of 170 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 118 = 1 remainder 52 |
| 2 | 118 ÷ 52 = 2 remainder 14 |
| 3 | 52 ÷ 14 = 3 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 105 | 1785 |
| 32 and 26 | 416 |
| 99 and 20 | 1980 |
| 41 and 48 | 1968 |
| 191 and 175 | 33425 |