Least Common Multiple (LCM) of 47 and 113
The least common multiple (LCM) of 47 and 113 is 5311.
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 113?
First, calculate the GCD of 47 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 113 = 0 remainder 47 |
| 2 | 113 ÷ 47 = 2 remainder 19 |
| 3 | 47 ÷ 19 = 2 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 108 | 756 |
| 34 and 151 | 5134 |
| 130 and 60 | 780 |
| 176 and 199 | 35024 |
| 92 and 165 | 15180 |