Least Common Multiple (LCM) of 195 and 45
The least common multiple (LCM) of 195 and 45 is 585.
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 45?
First, calculate the GCD of 195 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 45 = 4 remainder 15 |
| 2 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 163 | 23635 |
| 102 and 173 | 17646 |
| 113 and 100 | 11300 |
| 104 and 193 | 20072 |
| 165 and 139 | 22935 |