Least Common Multiple (LCM) of 103 and 65
The least common multiple (LCM) of 103 and 65 is 6695.
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 103 and 65?
First, calculate the GCD of 103 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 65 = 1 remainder 38 |
| 2 | 65 ÷ 38 = 1 remainder 27 |
| 3 | 38 ÷ 27 = 1 remainder 11 |
| 4 | 27 ÷ 11 = 2 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 33 | 528 |
| 98 and 90 | 4410 |
| 20 and 68 | 340 |
| 77 and 75 | 5775 |
| 58 and 22 | 638 |