Least Common Multiple (LCM) of 106 and 131
The least common multiple (LCM) of 106 and 131 is 13886.
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 106 and 131?
First, calculate the GCD of 106 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 131 = 0 remainder 106 |
| 2 | 131 ÷ 106 = 1 remainder 25 |
| 3 | 106 ÷ 25 = 4 remainder 6 |
| 4 | 25 ÷ 6 = 4 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 20 | 140 |
| 155 and 97 | 15035 |
| 59 and 154 | 9086 |
| 97 and 101 | 9797 |
| 107 and 113 | 12091 |