Least Common Multiple (LCM) of 31 and 83
The least common multiple (LCM) of 31 and 83 is 2573.
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 31 and 83?
First, calculate the GCD of 31 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 83 = 0 remainder 31 |
| 2 | 83 ÷ 31 = 2 remainder 21 |
| 3 | 31 ÷ 21 = 1 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 82 | 11070 |
| 103 and 49 | 5047 |
| 127 and 102 | 12954 |
| 119 and 184 | 21896 |
| 37 and 63 | 2331 |