Least Common Multiple (LCM) of 196 and 111
The least common multiple (LCM) of 196 and 111 is 21756.
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 111?
First, calculate the GCD of 196 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 111 = 1 remainder 85 |
| 2 | 111 ÷ 85 = 1 remainder 26 |
| 3 | 85 ÷ 26 = 3 remainder 7 |
| 4 | 26 ÷ 7 = 3 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 124 | 620 |
| 10 and 189 | 1890 |
| 55 and 15 | 165 |
| 54 and 91 | 4914 |
| 57 and 36 | 684 |