Least Common Multiple (LCM) of 109 and 196
The least common multiple (LCM) of 109 and 196 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 109 and 196?
First, calculate the GCD of 109 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 196 = 0 remainder 109 |
| 2 | 196 ÷ 109 = 1 remainder 87 |
| 3 | 109 ÷ 87 = 1 remainder 22 |
| 4 | 87 ÷ 22 = 3 remainder 21 |
| 5 | 22 ÷ 21 = 1 remainder 1 |
| 6 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 79 | 7821 |
| 100 and 87 | 8700 |
| 183 and 189 | 11529 |
| 52 and 56 | 728 |
| 55 and 54 | 2970 |