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 |
|---|---|
| 38 and 19 | 38 |
| 161 and 162 | 26082 |
| 148 and 57 | 8436 |
| 101 and 114 | 11514 |
| 89 and 18 | 1602 |