Least Common Multiple (LCM) of 65 and 77
The least common multiple (LCM) of 65 and 77 is 5005.
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 65 and 77?
First, calculate the GCD of 65 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 77 = 0 remainder 65 |
| 2 | 77 ÷ 65 = 1 remainder 12 |
| 3 | 65 ÷ 12 = 5 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 191 | 31897 |
| 123 and 124 | 15252 |
| 49 and 190 | 9310 |
| 64 and 105 | 6720 |
| 116 and 132 | 3828 |