Least Common Multiple (LCM) of 65 and 79
The least common multiple (LCM) of 65 and 79 is 5135.
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 79?
First, calculate the GCD of 65 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 79 = 0 remainder 65 |
| 2 | 79 ÷ 65 = 1 remainder 14 |
| 3 | 65 ÷ 14 = 4 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 141 | 11139 |
| 182 and 189 | 4914 |
| 151 and 12 | 1812 |
| 80 and 193 | 15440 |
| 40 and 103 | 4120 |