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 |
|---|---|
| 127 and 29 | 3683 |
| 67 and 160 | 10720 |
| 198 and 19 | 3762 |
| 107 and 166 | 17762 |
| 105 and 97 | 10185 |