Least Common Multiple (LCM) of 170 and 192
The least common multiple (LCM) of 170 and 192 is 16320.
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 192?
First, calculate the GCD of 170 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 192 = 0 remainder 170 |
| 2 | 192 ÷ 170 = 1 remainder 22 |
| 3 | 170 ÷ 22 = 7 remainder 16 |
| 4 | 22 ÷ 16 = 1 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 188 | 4700 |
| 116 and 46 | 2668 |
| 125 and 42 | 5250 |
| 63 and 147 | 441 |
| 160 and 107 | 17120 |