Least Common Multiple (LCM) of 81 and 196
The least common multiple (LCM) of 81 and 196 is 15876.
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 81 and 196?
First, calculate the GCD of 81 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 196 = 0 remainder 81 |
| 2 | 196 ÷ 81 = 2 remainder 34 |
| 3 | 81 ÷ 34 = 2 remainder 13 |
| 4 | 34 ÷ 13 = 2 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 16 | 48 |
| 56 and 17 | 952 |
| 54 and 35 | 1890 |
| 108 and 198 | 1188 |
| 143 and 54 | 7722 |