Least Common Multiple (LCM) of 47 and 121
The least common multiple (LCM) of 47 and 121 is 5687.
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 121?
First, calculate the GCD of 47 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 121 = 0 remainder 47 |
| 2 | 121 ÷ 47 = 2 remainder 27 |
| 3 | 47 ÷ 27 = 1 remainder 20 |
| 4 | 27 ÷ 20 = 1 remainder 7 |
| 5 | 20 ÷ 7 = 2 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 11 | 2200 |
| 125 and 60 | 1500 |
| 113 and 110 | 12430 |
| 142 and 175 | 24850 |
| 120 and 199 | 23880 |