Least Common Multiple (LCM) of 77 and 17
The least common multiple (LCM) of 77 and 17 is 1309.
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 17?
First, calculate the GCD of 77 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 17 = 4 remainder 9 |
| 2 | 17 ÷ 9 = 1 remainder 8 |
| 3 | 9 ÷ 8 = 1 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 97 | 19012 |
| 103 and 15 | 1545 |
| 124 and 83 | 10292 |
| 143 and 81 | 11583 |
| 50 and 200 | 200 |