Least Common Multiple (LCM) of 196 and 107
The least common multiple (LCM) of 196 and 107 is 20972.
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 107?
First, calculate the GCD of 196 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 107 = 1 remainder 89 |
| 2 | 107 ÷ 89 = 1 remainder 18 |
| 3 | 89 ÷ 18 = 4 remainder 17 |
| 4 | 18 ÷ 17 = 1 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 116 | 1972 |
| 141 and 146 | 20586 |
| 60 and 54 | 540 |
| 123 and 185 | 22755 |
| 147 and 136 | 19992 |