Least Common Multiple (LCM) of 195 and 105
The least common multiple (LCM) of 195 and 105 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 195 and 105?
First, calculate the GCD of 195 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 105 = 1 remainder 90 |
| 2 | 105 ÷ 90 = 1 remainder 15 |
| 3 | 90 ÷ 15 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 53 | 6731 |
| 32 and 104 | 416 |
| 122 and 133 | 16226 |
| 103 and 111 | 11433 |
| 188 and 188 | 188 |