Least Common Multiple (LCM) of 112 and 131
The least common multiple (LCM) of 112 and 131 is 14672.
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 112 and 131?
First, calculate the GCD of 112 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 131 = 0 remainder 112 |
| 2 | 131 ÷ 112 = 1 remainder 19 |
| 3 | 112 ÷ 19 = 5 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 66 | 132 |
| 11 and 31 | 341 |
| 36 and 106 | 1908 |
| 59 and 126 | 7434 |
| 152 and 91 | 13832 |