Least Common Multiple (LCM) of 131 and 68
The least common multiple (LCM) of 131 and 68 is 8908.
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 68?
First, calculate the GCD of 131 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 68 = 1 remainder 63 |
| 2 | 68 ÷ 63 = 1 remainder 5 |
| 3 | 63 ÷ 5 = 12 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 |
|---|---|
| 85 and 64 | 5440 |
| 196 and 36 | 1764 |
| 10 and 114 | 570 |
| 127 and 76 | 9652 |
| 168 and 41 | 6888 |