Least Common Multiple (LCM) of 47 and 167
The least common multiple (LCM) of 47 and 167 is 7849.
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 167?
First, calculate the GCD of 47 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 167 = 0 remainder 47 |
| 2 | 167 ÷ 47 = 3 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 |
|---|---|
| 185 and 163 | 30155 |
| 68 and 51 | 204 |
| 72 and 199 | 14328 |
| 198 and 78 | 2574 |
| 185 and 52 | 9620 |