Least Common Multiple (LCM) of 111 and 196
The least common multiple (LCM) of 111 and 196 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 111 and 196?
First, calculate the GCD of 111 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 196 = 0 remainder 111 |
| 2 | 196 ÷ 111 = 1 remainder 85 |
| 3 | 111 ÷ 85 = 1 remainder 26 |
| 4 | 85 ÷ 26 = 3 remainder 7 |
| 5 | 26 ÷ 7 = 3 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 196 | 3332 |
| 49 and 16 | 784 |
| 142 and 14 | 994 |
| 198 and 199 | 39402 |
| 115 and 43 | 4945 |