Least Common Multiple (LCM) of 77 and 68
The least common multiple (LCM) of 77 and 68 is 5236.
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 68?
First, calculate the GCD of 77 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 68 = 1 remainder 9 |
| 2 | 68 ÷ 9 = 7 remainder 5 |
| 3 | 9 ÷ 5 = 1 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 104 | 1248 |
| 59 and 71 | 4189 |
| 88 and 92 | 2024 |
| 180 and 184 | 8280 |
| 24 and 40 | 120 |