Least Common Multiple (LCM) of 47 and 129
The least common multiple (LCM) of 47 and 129 is 6063.
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 129?
First, calculate the GCD of 47 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 129 = 0 remainder 47 |
| 2 | 129 ÷ 47 = 2 remainder 35 |
| 3 | 47 ÷ 35 = 1 remainder 12 |
| 4 | 35 ÷ 12 = 2 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 17 | 2329 |
| 182 and 67 | 12194 |
| 142 and 55 | 7810 |
| 180 and 75 | 900 |
| 53 and 117 | 6201 |