Least Common Multiple (LCM) of 96 and 116
The least common multiple (LCM) of 96 and 116 is 2784.
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 116?
First, calculate the GCD of 96 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 116 = 0 remainder 96 |
| 2 | 116 ÷ 96 = 1 remainder 20 |
| 3 | 96 ÷ 20 = 4 remainder 16 |
| 4 | 20 ÷ 16 = 1 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 156 | 3900 |
| 180 and 82 | 7380 |
| 37 and 57 | 2109 |
| 92 and 33 | 3036 |
| 133 and 21 | 399 |