Least Common Multiple (LCM) of 47 and 73
The least common multiple (LCM) of 47 and 73 is 3431.
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 73?
First, calculate the GCD of 47 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 73 = 0 remainder 47 |
| 2 | 73 ÷ 47 = 1 remainder 26 |
| 3 | 47 ÷ 26 = 1 remainder 21 |
| 4 | 26 ÷ 21 = 1 remainder 5 |
| 5 | 21 ÷ 5 = 4 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 135 | 24030 |
| 12 and 113 | 1356 |
| 64 and 149 | 9536 |
| 85 and 73 | 6205 |
| 75 and 59 | 4425 |