Least Common Multiple (LCM) of 113 and 193
The least common multiple (LCM) of 113 and 193 is 21809.
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 113 and 193?
First, calculate the GCD of 113 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 193 = 0 remainder 113 |
| 2 | 193 ÷ 113 = 1 remainder 80 |
| 3 | 113 ÷ 80 = 1 remainder 33 |
| 4 | 80 ÷ 33 = 2 remainder 14 |
| 5 | 33 ÷ 14 = 2 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 30 | 510 |
| 63 and 147 | 441 |
| 175 and 83 | 14525 |
| 80 and 125 | 2000 |
| 157 and 56 | 8792 |