Least Common Multiple (LCM) of 47 and 68
The least common multiple (LCM) of 47 and 68 is 3196.
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 68?
First, calculate the GCD of 47 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 68 = 0 remainder 47 |
| 2 | 68 ÷ 47 = 1 remainder 21 |
| 3 | 47 ÷ 21 = 2 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 200 | 200 |
| 168 and 188 | 7896 |
| 103 and 19 | 1957 |
| 135 and 60 | 540 |
| 33 and 19 | 627 |