Least Common Multiple (LCM) of 77 and 97
The least common multiple (LCM) of 77 and 97 is 7469.
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 97?
First, calculate the GCD of 77 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 97 = 0 remainder 77 |
| 2 | 97 ÷ 77 = 1 remainder 20 |
| 3 | 77 ÷ 20 = 3 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 89 | 3115 |
| 184 and 45 | 8280 |
| 142 and 63 | 8946 |
| 170 and 98 | 8330 |
| 96 and 39 | 1248 |