Least Common Multiple (LCM) of 65 and 19
The least common multiple (LCM) of 65 and 19 is 1235.
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 19?
First, calculate the GCD of 65 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 19 = 3 remainder 8 |
| 2 | 19 ÷ 8 = 2 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 115 | 7820 |
| 118 and 14 | 826 |
| 146 and 173 | 25258 |
| 29 and 92 | 2668 |
| 162 and 69 | 3726 |