Least Common Multiple (LCM) of 77 and 83
The least common multiple (LCM) of 77 and 83 is 6391.
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 83?
First, calculate the GCD of 77 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 83 = 0 remainder 77 |
| 2 | 83 ÷ 77 = 1 remainder 6 |
| 3 | 77 ÷ 6 = 12 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 83 | 10375 |
| 138 and 72 | 1656 |
| 79 and 121 | 9559 |
| 173 and 146 | 25258 |
| 73 and 123 | 8979 |