Least Common Multiple (LCM) of 131 and 83
The least common multiple (LCM) of 131 and 83 is 10873.
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 83?
First, calculate the GCD of 131 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 83 = 1 remainder 48 |
| 2 | 83 ÷ 48 = 1 remainder 35 |
| 3 | 48 ÷ 35 = 1 remainder 13 |
| 4 | 35 ÷ 13 = 2 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 100 | 1700 |
| 60 and 71 | 4260 |
| 141 and 87 | 4089 |
| 145 and 90 | 2610 |
| 170 and 189 | 32130 |