Least Common Multiple (LCM) of 83 and 97
The least common multiple (LCM) of 83 and 97 is 8051.
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 83 and 97?
First, calculate the GCD of 83 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 97 = 0 remainder 83 |
| 2 | 97 ÷ 83 = 1 remainder 14 |
| 3 | 83 ÷ 14 = 5 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 136 | 15368 |
| 100 and 173 | 17300 |
| 91 and 58 | 5278 |
| 123 and 41 | 123 |
| 104 and 15 | 1560 |