Least Common Multiple (LCM) of 47 and 195
The least common multiple (LCM) of 47 and 195 is 9165.
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 195?
First, calculate the GCD of 47 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 195 = 0 remainder 47 |
| 2 | 195 ÷ 47 = 4 remainder 7 |
| 3 | 47 ÷ 7 = 6 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 105 | 3360 |
| 12 and 33 | 132 |
| 122 and 182 | 11102 |
| 146 and 77 | 11242 |
| 170 and 76 | 6460 |