Least Common Multiple (LCM) of 116 and 196
The least common multiple (LCM) of 116 and 196 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 116 and 196?
First, calculate the GCD of 116 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 196 = 0 remainder 116 |
| 2 | 196 ÷ 116 = 1 remainder 80 |
| 3 | 116 ÷ 80 = 1 remainder 36 |
| 4 | 80 ÷ 36 = 2 remainder 8 |
| 5 | 36 ÷ 8 = 4 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 25 | 4550 |
| 175 and 49 | 1225 |
| 40 and 104 | 520 |
| 64 and 192 | 192 |
| 184 and 30 | 2760 |