Least Common Multiple (LCM) of 74 and 193
The least common multiple (LCM) of 74 and 193 is 14282.
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 74 and 193?
First, calculate the GCD of 74 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 193 = 0 remainder 74 |
| 2 | 193 ÷ 74 = 2 remainder 45 |
| 3 | 74 ÷ 45 = 1 remainder 29 |
| 4 | 45 ÷ 29 = 1 remainder 16 |
| 5 | 29 ÷ 16 = 1 remainder 13 |
| 6 | 16 ÷ 13 = 1 remainder 3 |
| 7 | 13 ÷ 3 = 4 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 126 | 12978 |
| 86 and 54 | 2322 |
| 172 and 128 | 5504 |
| 25 and 196 | 4900 |
| 199 and 158 | 31442 |