Least Common Multiple (LCM) of 131 and 113
The least common multiple (LCM) of 131 and 113 is 14803.
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 113?
First, calculate the GCD of 131 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 113 = 1 remainder 18 |
| 2 | 113 ÷ 18 = 6 remainder 5 |
| 3 | 18 ÷ 5 = 3 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 113 | 15142 |
| 160 and 121 | 19360 |
| 59 and 126 | 7434 |
| 123 and 80 | 9840 |
| 56 and 131 | 7336 |