Least Common Multiple (LCM) of 47 and 57
The least common multiple (LCM) of 47 and 57 is 2679.
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 57?
First, calculate the GCD of 47 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 57 = 0 remainder 47 |
| 2 | 57 ÷ 47 = 1 remainder 10 |
| 3 | 47 ÷ 10 = 4 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 |
|---|---|
| 109 and 44 | 4796 |
| 37 and 46 | 1702 |
| 121 and 200 | 24200 |
| 148 and 193 | 28564 |
| 132 and 162 | 3564 |