Least Common Multiple (LCM) of 114 and 47
The least common multiple (LCM) of 114 and 47 is 5358.
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 114 and 47?
First, calculate the GCD of 114 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 47 = 2 remainder 20 |
| 2 | 47 ÷ 20 = 2 remainder 7 |
| 3 | 20 ÷ 7 = 2 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 145 | 4930 |
| 131 and 163 | 21353 |
| 40 and 105 | 840 |
| 68 and 189 | 12852 |
| 100 and 81 | 8100 |