Least Common Multiple (LCM) of 168 and 47
The least common multiple (LCM) of 168 and 47 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 168 and 47?
First, calculate the GCD of 168 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 47 = 3 remainder 27 |
| 2 | 47 ÷ 27 = 1 remainder 20 |
| 3 | 27 ÷ 20 = 1 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 39 | 4290 |
| 122 and 151 | 18422 |
| 130 and 128 | 8320 |
| 20 and 70 | 140 |
| 102 and 187 | 1122 |