Least Common Multiple (LCM) of 193 and 180
The least common multiple (LCM) of 193 and 180 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 193 and 180?
First, calculate the GCD of 193 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 180 = 1 remainder 13 |
| 2 | 180 ÷ 13 = 13 remainder 11 |
| 3 | 13 ÷ 11 = 1 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 100 | 3300 |
| 129 and 23 | 2967 |
| 10 and 140 | 140 |
| 153 and 154 | 23562 |
| 95 and 170 | 3230 |