Least Common Multiple (LCM) of 196 and 109
The least common multiple (LCM) of 196 and 109 is 21364.
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 109?
First, calculate the GCD of 196 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 109 = 1 remainder 87 |
| 2 | 109 ÷ 87 = 1 remainder 22 |
| 3 | 87 ÷ 22 = 3 remainder 21 |
| 4 | 22 ÷ 21 = 1 remainder 1 |
| 5 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 49 | 4361 |
| 21 and 96 | 672 |
| 75 and 94 | 7050 |
| 137 and 10 | 1370 |
| 73 and 17 | 1241 |