Least Common Multiple (LCM) of 96 and 133
The least common multiple (LCM) of 96 and 133 is 12768.
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 96 and 133?
First, calculate the GCD of 96 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 133 = 0 remainder 96 |
| 2 | 133 ÷ 96 = 1 remainder 37 |
| 3 | 96 ÷ 37 = 2 remainder 22 |
| 4 | 37 ÷ 22 = 1 remainder 15 |
| 5 | 22 ÷ 15 = 1 remainder 7 |
| 6 | 15 ÷ 7 = 2 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 49 | 7742 |
| 69 and 101 | 6969 |
| 114 and 53 | 6042 |
| 10 and 42 | 210 |
| 87 and 165 | 4785 |