Least Common Multiple (LCM) of 131 and 112
The least common multiple (LCM) of 131 and 112 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 131 and 112?
First, calculate the GCD of 131 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 112 = 1 remainder 19 |
| 2 | 112 ÷ 19 = 5 remainder 17 |
| 3 | 19 ÷ 17 = 1 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 34 | 34 |
| 20 and 70 | 140 |
| 94 and 106 | 4982 |
| 71 and 145 | 10295 |
| 96 and 170 | 8160 |