Least Common Multiple (LCM) of 110 and 131
The least common multiple (LCM) of 110 and 131 is 14410.
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 110 and 131?
First, calculate the GCD of 110 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 131 = 0 remainder 110 |
| 2 | 131 ÷ 110 = 1 remainder 21 |
| 3 | 110 ÷ 21 = 5 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 113 | 12091 |
| 112 and 182 | 1456 |
| 100 and 161 | 16100 |
| 11 and 94 | 1034 |
| 125 and 192 | 24000 |