Least Common Multiple (LCM) of 102 and 195
The least common multiple (LCM) of 102 and 195 is 6630.
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 102 and 195?
First, calculate the GCD of 102 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 195 = 0 remainder 102 |
| 2 | 195 ÷ 102 = 1 remainder 93 |
| 3 | 102 ÷ 93 = 1 remainder 9 |
| 4 | 93 ÷ 9 = 10 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 77 | 7700 |
| 186 and 115 | 21390 |
| 161 and 106 | 17066 |
| 12 and 122 | 732 |
| 45 and 180 | 180 |