Least Common Multiple (LCM) of 99 and 131
The least common multiple (LCM) of 99 and 131 is 12969.
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 99 and 131?
First, calculate the GCD of 99 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 131 = 0 remainder 99 |
| 2 | 131 ÷ 99 = 1 remainder 32 |
| 3 | 99 ÷ 32 = 3 remainder 3 |
| 4 | 32 ÷ 3 = 10 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 188 | 3196 |
| 55 and 185 | 2035 |
| 119 and 133 | 2261 |
| 162 and 83 | 13446 |
| 27 and 104 | 2808 |