Least Common Multiple (LCM) of 133 and 58
The least common multiple (LCM) of 133 and 58 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 133 and 58?
First, calculate the GCD of 133 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 58 = 2 remainder 17 |
| 2 | 58 ÷ 17 = 3 remainder 7 |
| 3 | 17 ÷ 7 = 2 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 17 | 51 |
| 108 and 102 | 1836 |
| 13 and 146 | 1898 |
| 129 and 82 | 10578 |
| 113 and 10 | 1130 |