Least Common Multiple (LCM) of 81 and 197
The least common multiple (LCM) of 81 and 197 is 15957.
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 197?
First, calculate the GCD of 81 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 197 = 0 remainder 81 |
| 2 | 197 ÷ 81 = 2 remainder 35 |
| 3 | 81 ÷ 35 = 2 remainder 11 |
| 4 | 35 ÷ 11 = 3 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 53 | 5936 |
| 60 and 118 | 3540 |
| 134 and 88 | 5896 |
| 59 and 13 | 767 |
| 193 and 31 | 5983 |