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 |
|---|---|
| 103 and 130 | 13390 |
| 98 and 192 | 9408 |
| 22 and 71 | 1562 |
| 185 and 157 | 29045 |
| 70 and 158 | 5530 |