Least Common Multiple (LCM) of 75 and 77
The least common multiple (LCM) of 75 and 77 is 5775.
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 75 and 77?
First, calculate the GCD of 75 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 77 = 0 remainder 75 |
| 2 | 77 ÷ 75 = 1 remainder 2 |
| 3 | 75 ÷ 2 = 37 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 158 | 8216 |
| 180 and 115 | 4140 |
| 96 and 71 | 6816 |
| 197 and 36 | 7092 |
| 45 and 56 | 2520 |