Least Common Multiple (LCM) of 47 and 131
The least common multiple (LCM) of 47 and 131 is 6157.
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 131?
First, calculate the GCD of 47 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 131 = 0 remainder 47 |
| 2 | 131 ÷ 47 = 2 remainder 37 |
| 3 | 47 ÷ 37 = 1 remainder 10 |
| 4 | 37 ÷ 10 = 3 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 44 | 132 |
| 22 and 108 | 1188 |
| 148 and 14 | 1036 |
| 141 and 196 | 27636 |
| 119 and 31 | 3689 |