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 |
|---|---|
| 104 and 79 | 8216 |
| 121 and 182 | 22022 |
| 170 and 164 | 13940 |
| 162 and 84 | 2268 |
| 121 and 115 | 13915 |