Least Common Multiple (LCM) of 47 and 168
The least common multiple (LCM) of 47 and 168 is 7896.
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 168?
First, calculate the GCD of 47 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 168 = 0 remainder 47 |
| 2 | 168 ÷ 47 = 3 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 |
|---|---|
| 198 and 57 | 3762 |
| 107 and 102 | 10914 |
| 100 and 58 | 2900 |
| 184 and 51 | 9384 |
| 46 and 25 | 1150 |