Least Common Multiple (LCM) of 83 and 91
The least common multiple (LCM) of 83 and 91 is 7553.
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 91?
First, calculate the GCD of 83 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 91 = 0 remainder 83 |
| 2 | 91 ÷ 83 = 1 remainder 8 |
| 3 | 83 ÷ 8 = 10 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 142 | 25702 |
| 142 and 28 | 1988 |
| 80 and 94 | 3760 |
| 99 and 47 | 4653 |
| 12 and 51 | 204 |