Least Common Multiple (LCM) of 105 and 65
The least common multiple (LCM) of 105 and 65 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 105 and 65?
First, calculate the GCD of 105 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 65 = 1 remainder 40 |
| 2 | 65 ÷ 40 = 1 remainder 25 |
| 3 | 40 ÷ 25 = 1 remainder 15 |
| 4 | 25 ÷ 15 = 1 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 14 | 1610 |
| 182 and 102 | 9282 |
| 141 and 106 | 14946 |
| 164 and 187 | 30668 |
| 113 and 18 | 2034 |