Least Common Multiple (LCM) of 110 and 193
The least common multiple (LCM) of 110 and 193 is 21230.
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 110 and 193?
First, calculate the GCD of 110 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 193 = 0 remainder 110 |
| 2 | 193 ÷ 110 = 1 remainder 83 |
| 3 | 110 ÷ 83 = 1 remainder 27 |
| 4 | 83 ÷ 27 = 3 remainder 2 |
| 5 | 27 ÷ 2 = 13 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 53 | 8957 |
| 51 and 54 | 918 |
| 61 and 137 | 8357 |
| 147 and 19 | 2793 |
| 53 and 75 | 3975 |