Least Common Multiple (LCM) of 116 and 133
The least common multiple (LCM) of 116 and 133 is 15428.
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 133?
First, calculate the GCD of 116 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 133 = 0 remainder 116 |
| 2 | 133 ÷ 116 = 1 remainder 17 |
| 3 | 116 ÷ 17 = 6 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 |
|---|---|
| 49 and 46 | 2254 |
| 102 and 58 | 2958 |
| 157 and 175 | 27475 |
| 171 and 49 | 8379 |
| 36 and 199 | 7164 |