Least Common Multiple (LCM) of 131 and 84
The least common multiple (LCM) of 131 and 84 is 11004.
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 84?
First, calculate the GCD of 131 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 84 = 1 remainder 47 |
| 2 | 84 ÷ 47 = 1 remainder 37 |
| 3 | 47 ÷ 37 = 1 remainder 10 |
| 4 | 37 ÷ 10 = 3 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 31 | 1426 |
| 116 and 105 | 12180 |
| 152 and 118 | 8968 |
| 186 and 12 | 372 |
| 107 and 155 | 16585 |