Least Common Multiple (LCM) of 58 and 133
The least common multiple (LCM) of 58 and 133 is 7714.
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 58 and 133?
First, calculate the GCD of 58 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 133 = 0 remainder 58 |
| 2 | 133 ÷ 58 = 2 remainder 17 |
| 3 | 58 ÷ 17 = 3 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 26 | 754 |
| 71 and 53 | 3763 |
| 31 and 10 | 310 |
| 122 and 177 | 21594 |
| 54 and 31 | 1674 |