Least Common Multiple (LCM) of 99 and 116
The least common multiple (LCM) of 99 and 116 is 11484.
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 116?
First, calculate the GCD of 99 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 116 = 0 remainder 99 |
| 2 | 116 ÷ 99 = 1 remainder 17 |
| 3 | 99 ÷ 17 = 5 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 16 | 16 |
| 175 and 103 | 18025 |
| 192 and 198 | 6336 |
| 51 and 74 | 3774 |
| 120 and 86 | 5160 |