Least Common Multiple (LCM) of 126 and 103
The least common multiple (LCM) of 126 and 103 is 12978.
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 103?
First, calculate the GCD of 126 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 103 = 1 remainder 23 |
| 2 | 103 ÷ 23 = 4 remainder 11 |
| 3 | 23 ÷ 11 = 2 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 77 | 6699 |
| 80 and 86 | 3440 |
| 188 and 14 | 1316 |
| 141 and 138 | 6486 |
| 181 and 62 | 11222 |