Least Common Multiple (LCM) of 102 and 109
The least common multiple (LCM) of 102 and 109 is 11118.
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 109?
First, calculate the GCD of 102 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 109 = 0 remainder 102 |
| 2 | 109 ÷ 102 = 1 remainder 7 |
| 3 | 102 ÷ 7 = 14 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 35 | 945 |
| 105 and 193 | 20265 |
| 125 and 137 | 17125 |
| 61 and 72 | 4392 |
| 117 and 85 | 9945 |