Least Common Multiple (LCM) of 193 and 170
The least common multiple (LCM) of 193 and 170 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 193 and 170?
First, calculate the GCD of 193 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 170 = 1 remainder 23 |
| 2 | 170 ÷ 23 = 7 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 160 | 9120 |
| 135 and 82 | 11070 |
| 85 and 102 | 510 |
| 169 and 158 | 26702 |
| 189 and 162 | 1134 |