Least Common Multiple (LCM) of 65 and 51
The least common multiple (LCM) of 65 and 51 is 3315.
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 51?
First, calculate the GCD of 65 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 51 = 1 remainder 14 |
| 2 | 51 ÷ 14 = 3 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 66 | 9570 |
| 118 and 179 | 21122 |
| 91 and 85 | 7735 |
| 14 and 119 | 238 |
| 57 and 147 | 2793 |