Least Common Multiple (LCM) of 196 and 116
The least common multiple (LCM) of 196 and 116 is 5684.
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 196 and 116?
First, calculate the GCD of 196 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 116 = 1 remainder 80 |
| 2 | 116 ÷ 80 = 1 remainder 36 |
| 3 | 80 ÷ 36 = 2 remainder 8 |
| 4 | 36 ÷ 8 = 4 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 117 | 17082 |
| 89 and 56 | 4984 |
| 175 and 185 | 6475 |
| 63 and 197 | 12411 |
| 16 and 75 | 1200 |