Least Common Multiple (LCM) of 193 and 108
The least common multiple (LCM) of 193 and 108 is 20844.
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 108?
First, calculate the GCD of 193 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 108 = 1 remainder 85 |
| 2 | 108 ÷ 85 = 1 remainder 23 |
| 3 | 85 ÷ 23 = 3 remainder 16 |
| 4 | 23 ÷ 16 = 1 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 31 | 1116 |
| 173 and 126 | 21798 |
| 180 and 113 | 20340 |
| 137 and 61 | 8357 |
| 169 and 146 | 24674 |