Least Common Multiple (LCM) of 105 and 195
The least common multiple (LCM) of 105 and 195 is 1365.
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 105 and 195?
First, calculate the GCD of 105 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 195 = 0 remainder 105 |
| 2 | 195 ÷ 105 = 1 remainder 90 |
| 3 | 105 ÷ 90 = 1 remainder 15 |
| 4 | 90 ÷ 15 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 181 | 5973 |
| 46 and 109 | 5014 |
| 114 and 159 | 6042 |
| 82 and 58 | 2378 |
| 107 and 140 | 14980 |