Least Common Multiple (LCM) of 116 and 99
The least common multiple (LCM) of 116 and 99 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 116 and 99?
First, calculate the GCD of 116 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 99 = 1 remainder 17 |
| 2 | 99 ÷ 17 = 5 remainder 14 |
| 3 | 17 ÷ 14 = 1 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 41 | 5986 |
| 130 and 139 | 18070 |
| 153 and 147 | 7497 |
| 144 and 174 | 4176 |
| 23 and 200 | 4600 |