Least Common Multiple (LCM) of 168 and 193
The least common multiple (LCM) of 168 and 193 is 32424.
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 168 and 193?
First, calculate the GCD of 168 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 193 = 0 remainder 168 |
| 2 | 193 ÷ 168 = 1 remainder 25 |
| 3 | 168 ÷ 25 = 6 remainder 18 |
| 4 | 25 ÷ 18 = 1 remainder 7 |
| 5 | 18 ÷ 7 = 2 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 95 | 10165 |
| 83 and 154 | 12782 |
| 168 and 117 | 6552 |
| 187 and 113 | 21131 |
| 144 and 37 | 5328 |