Least Common Multiple (LCM) of 73 and 193
The least common multiple (LCM) of 73 and 193 is 14089.
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 73 and 193?
First, calculate the GCD of 73 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 193 = 0 remainder 73 |
| 2 | 193 ÷ 73 = 2 remainder 47 |
| 3 | 73 ÷ 47 = 1 remainder 26 |
| 4 | 47 ÷ 26 = 1 remainder 21 |
| 5 | 26 ÷ 21 = 1 remainder 5 |
| 6 | 21 ÷ 5 = 4 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 168 | 1680 |
| 90 and 123 | 3690 |
| 122 and 186 | 11346 |
| 36 and 38 | 684 |
| 143 and 156 | 1716 |