Least Common Multiple (LCM) of 28 and 65
The least common multiple (LCM) of 28 and 65 is 1820.
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 28 and 65?
First, calculate the GCD of 28 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 28 ÷ 65 = 0 remainder 28 |
| 2 | 65 ÷ 28 = 2 remainder 9 |
| 3 | 28 ÷ 9 = 3 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 37 | 2812 |
| 156 and 153 | 7956 |
| 112 and 129 | 14448 |
| 105 and 136 | 14280 |
| 120 and 183 | 7320 |