Least Common Multiple (LCM) of 107 and 196
The least common multiple (LCM) of 107 and 196 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 107 and 196?
First, calculate the GCD of 107 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 196 = 0 remainder 107 |
| 2 | 196 ÷ 107 = 1 remainder 89 |
| 3 | 107 ÷ 89 = 1 remainder 18 |
| 4 | 89 ÷ 18 = 4 remainder 17 |
| 5 | 18 ÷ 17 = 1 remainder 1 |
| 6 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 53 | 3233 |
| 195 and 104 | 1560 |
| 56 and 175 | 1400 |
| 113 and 15 | 1695 |
| 163 and 67 | 10921 |