Least Common Multiple (LCM) of 170 and 193
The least common multiple (LCM) of 170 and 193 is 32810.
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 193?
First, calculate the GCD of 170 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 193 = 0 remainder 170 |
| 2 | 193 ÷ 170 = 1 remainder 23 |
| 3 | 170 ÷ 23 = 7 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 13 | 533 |
| 16 and 84 | 336 |
| 105 and 38 | 3990 |
| 100 and 95 | 1900 |
| 169 and 196 | 33124 |