Least Common Multiple (LCM) of 47 and 133
The least common multiple (LCM) of 47 and 133 is 6251.
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 47 and 133?
First, calculate the GCD of 47 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 133 = 0 remainder 47 |
| 2 | 133 ÷ 47 = 2 remainder 39 |
| 3 | 47 ÷ 39 = 1 remainder 8 |
| 4 | 39 ÷ 8 = 4 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 40 | 2760 |
| 141 and 145 | 20445 |
| 198 and 125 | 24750 |
| 194 and 98 | 9506 |
| 39 and 151 | 5889 |