Least Common Multiple (LCM) of 131 and 47
The least common multiple (LCM) of 131 and 47 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 131 and 47?
First, calculate the GCD of 131 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 47 = 2 remainder 37 |
| 2 | 47 ÷ 37 = 1 remainder 10 |
| 3 | 37 ÷ 10 = 3 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 34 | 5610 |
| 131 and 59 | 7729 |
| 72 and 17 | 1224 |
| 17 and 52 | 884 |
| 115 and 111 | 12765 |