Least Common Multiple (LCM) of 65 and 76
The least common multiple (LCM) of 65 and 76 is 4940.
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 76?
First, calculate the GCD of 65 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 76 = 0 remainder 65 |
| 2 | 76 ÷ 65 = 1 remainder 11 |
| 3 | 65 ÷ 11 = 5 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 147 | 3234 |
| 65 and 166 | 10790 |
| 65 and 10 | 130 |
| 105 and 133 | 1995 |
| 174 and 132 | 3828 |