Least Common Multiple (LCM) of 44 and 65
The least common multiple (LCM) of 44 and 65 is 2860.
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 44 and 65?
First, calculate the GCD of 44 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 44 ÷ 65 = 0 remainder 44 |
| 2 | 65 ÷ 44 = 1 remainder 21 |
| 3 | 44 ÷ 21 = 2 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 29 | 696 |
| 144 and 172 | 6192 |
| 30 and 128 | 1920 |
| 157 and 129 | 20253 |
| 123 and 123 | 123 |