Least Common Multiple (LCM) of 45 and 193
The least common multiple (LCM) of 45 and 193 is 8685.
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 45 and 193?
First, calculate the GCD of 45 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 193 = 0 remainder 45 |
| 2 | 193 ÷ 45 = 4 remainder 13 |
| 3 | 45 ÷ 13 = 3 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 15 | 2010 |
| 171 and 157 | 26847 |
| 197 and 183 | 36051 |
| 135 and 168 | 7560 |
| 188 and 16 | 752 |