Least Common Multiple (LCM) of 77 and 103
The least common multiple (LCM) of 77 and 103 is 7931.
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 77 and 103?
First, calculate the GCD of 77 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 103 = 0 remainder 77 |
| 2 | 103 ÷ 77 = 1 remainder 26 |
| 3 | 77 ÷ 26 = 2 remainder 25 |
| 4 | 26 ÷ 25 = 1 remainder 1 |
| 5 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 90 | 1710 |
| 77 and 85 | 6545 |
| 117 and 89 | 10413 |
| 147 and 54 | 2646 |
| 172 and 15 | 2580 |