Least Common Multiple (LCM) of 103 and 195
The least common multiple (LCM) of 103 and 195 is 20085.
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 103 and 195?
First, calculate the GCD of 103 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 195 = 0 remainder 103 |
| 2 | 195 ÷ 103 = 1 remainder 92 |
| 3 | 103 ÷ 92 = 1 remainder 11 |
| 4 | 92 ÷ 11 = 8 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 93 | 2325 |
| 164 and 50 | 4100 |
| 179 and 137 | 24523 |
| 170 and 67 | 11390 |
| 76 and 127 | 9652 |