Least Common Multiple (LCM) of 195 and 111
The least common multiple (LCM) of 195 and 111 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 195 and 111?
First, calculate the GCD of 195 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 111 = 1 remainder 84 |
| 2 | 111 ÷ 84 = 1 remainder 27 |
| 3 | 84 ÷ 27 = 3 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 24 | 120 |
| 150 and 134 | 10050 |
| 118 and 133 | 15694 |
| 64 and 110 | 3520 |
| 68 and 149 | 10132 |