Least Common Multiple (LCM) of 65 and 105
The least common multiple (LCM) of 65 and 105 is 1365.
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 105?
First, calculate the GCD of 65 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 105 = 0 remainder 65 |
| 2 | 105 ÷ 65 = 1 remainder 40 |
| 3 | 65 ÷ 40 = 1 remainder 25 |
| 4 | 40 ÷ 25 = 1 remainder 15 |
| 5 | 25 ÷ 15 = 1 remainder 10 |
| 6 | 15 ÷ 10 = 1 remainder 5 |
| 7 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 21 | 3927 |
| 164 and 180 | 7380 |
| 11 and 107 | 1177 |
| 86 and 169 | 14534 |
| 51 and 135 | 2295 |