Least Common Multiple (LCM) of 113 and 126
The least common multiple (LCM) of 113 and 126 is 14238.
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 113 and 126?
First, calculate the GCD of 113 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 126 = 0 remainder 113 |
| 2 | 126 ÷ 113 = 1 remainder 13 |
| 3 | 113 ÷ 13 = 8 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 153 | 3060 |
| 188 and 137 | 25756 |
| 78 and 10 | 390 |
| 119 and 180 | 21420 |
| 159 and 181 | 28779 |