Least Common Multiple (LCM) of 59 and 133
The least common multiple (LCM) of 59 and 133 is 7847.
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 59 and 133?
First, calculate the GCD of 59 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 133 = 0 remainder 59 |
| 2 | 133 ÷ 59 = 2 remainder 15 |
| 3 | 59 ÷ 15 = 3 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 105 | 19005 |
| 86 and 125 | 10750 |
| 60 and 128 | 1920 |
| 193 and 36 | 6948 |
| 142 and 17 | 2414 |