Least Common Multiple (LCM) of 180 and 191
The least common multiple (LCM) of 180 and 191 is 34380.
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 191?
First, calculate the GCD of 180 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 191 = 0 remainder 180 |
| 2 | 191 ÷ 180 = 1 remainder 11 |
| 3 | 180 ÷ 11 = 16 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 54 | 108 |
| 138 and 199 | 27462 |
| 30 and 139 | 4170 |
| 95 and 94 | 8930 |
| 12 and 116 | 348 |