Least Common Multiple (LCM) of 47 and 77
The least common multiple (LCM) of 47 and 77 is 3619.
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 77?
First, calculate the GCD of 47 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 77 = 0 remainder 47 |
| 2 | 77 ÷ 47 = 1 remainder 30 |
| 3 | 47 ÷ 30 = 1 remainder 17 |
| 4 | 30 ÷ 17 = 1 remainder 13 |
| 5 | 17 ÷ 13 = 1 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 105 | 1785 |
| 177 and 89 | 15753 |
| 109 and 16 | 1744 |
| 102 and 174 | 2958 |
| 76 and 58 | 2204 |