Least Common Multiple (LCM) of 111 and 195
The least common multiple (LCM) of 111 and 195 is 7215.
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 111 and 195?
First, calculate the GCD of 111 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 195 = 0 remainder 111 |
| 2 | 195 ÷ 111 = 1 remainder 84 |
| 3 | 111 ÷ 84 = 1 remainder 27 |
| 4 | 84 ÷ 27 = 3 remainder 3 |
| 5 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 112 | 6832 |
| 179 and 83 | 14857 |
| 114 and 151 | 17214 |
| 63 and 165 | 3465 |
| 105 and 112 | 1680 |