Least Common Multiple (LCM) of 47 and 115
The least common multiple (LCM) of 47 and 115 is 5405.
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 115?
First, calculate the GCD of 47 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 115 = 0 remainder 47 |
| 2 | 115 ÷ 47 = 2 remainder 21 |
| 3 | 47 ÷ 21 = 2 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 26 | 910 |
| 197 and 156 | 30732 |
| 82 and 65 | 5330 |
| 130 and 166 | 10790 |
| 105 and 100 | 2100 |