Least Common Multiple (LCM) of 133 and 116
The least common multiple (LCM) of 133 and 116 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 133 and 116?
First, calculate the GCD of 133 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 116 = 1 remainder 17 |
| 2 | 116 ÷ 17 = 6 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 |
|---|---|
| 12 and 10 | 60 |
| 139 and 32 | 4448 |
| 191 and 136 | 25976 |
| 13 and 192 | 2496 |
| 65 and 153 | 9945 |