Least Common Multiple (LCM) of 196 and 117
The least common multiple (LCM) of 196 and 117 is 22932.
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 117?
First, calculate the GCD of 196 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 117 = 1 remainder 79 |
| 2 | 117 ÷ 79 = 1 remainder 38 |
| 3 | 79 ÷ 38 = 2 remainder 3 |
| 4 | 38 ÷ 3 = 12 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 65 | 2015 |
| 143 and 166 | 23738 |
| 50 and 81 | 4050 |
| 77 and 131 | 10087 |
| 189 and 171 | 3591 |