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 |
|---|---|
| 198 and 189 | 4158 |
| 39 and 165 | 2145 |
| 171 and 73 | 12483 |
| 107 and 30 | 3210 |
| 11 and 151 | 1661 |