Least Common Multiple (LCM) of 110 and 195
The least common multiple (LCM) of 110 and 195 is 4290.
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 110 and 195?
First, calculate the GCD of 110 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 195 = 0 remainder 110 |
| 2 | 195 ÷ 110 = 1 remainder 85 |
| 3 | 110 ÷ 85 = 1 remainder 25 |
| 4 | 85 ÷ 25 = 3 remainder 10 |
| 5 | 25 ÷ 10 = 2 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 25 | 3225 |
| 106 and 30 | 1590 |
| 162 and 149 | 24138 |
| 130 and 67 | 8710 |
| 191 and 31 | 5921 |