Least Common Multiple (LCM) of 193 and 121
The least common multiple (LCM) of 193 and 121 is 23353.
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 121?
First, calculate the GCD of 193 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 121 = 1 remainder 72 |
| 2 | 121 ÷ 72 = 1 remainder 49 |
| 3 | 72 ÷ 49 = 1 remainder 23 |
| 4 | 49 ÷ 23 = 2 remainder 3 |
| 5 | 23 ÷ 3 = 7 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 197 | 6501 |
| 172 and 135 | 23220 |
| 185 and 166 | 30710 |
| 45 and 51 | 765 |
| 72 and 132 | 792 |