Least Common Multiple (LCM) of 53 and 65
The least common multiple (LCM) of 53 and 65 is 3445.
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 53 and 65?
First, calculate the GCD of 53 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 65 = 0 remainder 53 |
| 2 | 65 ÷ 53 = 1 remainder 12 |
| 3 | 53 ÷ 12 = 4 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 45 | 3735 |
| 177 and 94 | 16638 |
| 25 and 137 | 3425 |
| 47 and 90 | 4230 |
| 19 and 98 | 1862 |