Least Common Multiple (LCM) of 99 and 181
The least common multiple (LCM) of 99 and 181 is 17919.
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 181?
First, calculate the GCD of 99 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 181 = 0 remainder 99 |
| 2 | 181 ÷ 99 = 1 remainder 82 |
| 3 | 99 ÷ 82 = 1 remainder 17 |
| 4 | 82 ÷ 17 = 4 remainder 14 |
| 5 | 17 ÷ 14 = 1 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 116 | 3596 |
| 11 and 100 | 1100 |
| 28 and 101 | 2828 |
| 129 and 113 | 14577 |
| 116 and 110 | 6380 |