Least Common Multiple (LCM) of 31 and 58
The least common multiple (LCM) of 31 and 58 is 1798.
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 58?
First, calculate the GCD of 31 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 58 = 0 remainder 31 |
| 2 | 58 ÷ 31 = 1 remainder 27 |
| 3 | 31 ÷ 27 = 1 remainder 4 |
| 4 | 27 ÷ 4 = 6 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 68 | 3128 |
| 147 and 123 | 6027 |
| 27 and 15 | 135 |
| 40 and 80 | 80 |
| 89 and 79 | 7031 |