Least Common Multiple (LCM) of 103 and 126
The least common multiple (LCM) of 103 and 126 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 103 and 126?
First, calculate the GCD of 103 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 126 = 0 remainder 103 |
| 2 | 126 ÷ 103 = 1 remainder 23 |
| 3 | 103 ÷ 23 = 4 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 58 | 3190 |
| 31 and 191 | 5921 |
| 30 and 130 | 390 |
| 101 and 93 | 9393 |
| 157 and 27 | 4239 |