Least Common Multiple (LCM) of 180 and 193
The least common multiple (LCM) of 180 and 193 is 34740.
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 180 and 193?
First, calculate the GCD of 180 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 193 = 0 remainder 180 |
| 2 | 193 ÷ 180 = 1 remainder 13 |
| 3 | 180 ÷ 13 = 13 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 39 | 117 |
| 196 and 16 | 784 |
| 177 and 117 | 6903 |
| 185 and 86 | 15910 |
| 171 and 126 | 2394 |