Least Common Multiple (LCM) of 89 and 196
The least common multiple (LCM) of 89 and 196 is 17444.
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 89 and 196?
First, calculate the GCD of 89 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 196 = 0 remainder 89 |
| 2 | 196 ÷ 89 = 2 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 |
|---|---|
| 113 and 178 | 20114 |
| 35 and 36 | 1260 |
| 142 and 182 | 12922 |
| 71 and 193 | 13703 |
| 181 and 126 | 22806 |