Least Common Multiple (LCM) of 102 and 108
The least common multiple (LCM) of 102 and 108 is 1836.
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 108?
First, calculate the GCD of 102 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 108 = 0 remainder 102 |
| 2 | 108 ÷ 102 = 1 remainder 6 |
| 3 | 102 ÷ 6 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 163 | 2771 |
| 109 and 38 | 4142 |
| 95 and 109 | 10355 |
| 196 and 75 | 14700 |
| 132 and 58 | 3828 |