Least Common Multiple (LCM) of 126 and 102
The least common multiple (LCM) of 126 and 102 is 2142.
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 126 and 102?
First, calculate the GCD of 126 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 102 = 1 remainder 24 |
| 2 | 102 ÷ 24 = 4 remainder 6 |
| 3 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 30 | 810 |
| 195 and 110 | 4290 |
| 197 and 100 | 19700 |
| 27 and 104 | 2808 |
| 129 and 97 | 12513 |