Least Common Multiple (LCM) of 11 and 193
The least common multiple (LCM) of 11 and 193 is 2123.
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 11 and 193?
First, calculate the GCD of 11 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 193 = 0 remainder 11 |
| 2 | 193 ÷ 11 = 17 remainder 6 |
| 3 | 11 ÷ 6 = 1 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 105 | 3465 |
| 156 and 31 | 4836 |
| 56 and 184 | 1288 |
| 106 and 143 | 15158 |
| 140 and 141 | 19740 |