Least Common Multiple (LCM) of 65 and 113
The least common multiple (LCM) of 65 and 113 is 7345.
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 113?
First, calculate the GCD of 65 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 113 = 0 remainder 65 |
| 2 | 113 ÷ 65 = 1 remainder 48 |
| 3 | 65 ÷ 48 = 1 remainder 17 |
| 4 | 48 ÷ 17 = 2 remainder 14 |
| 5 | 17 ÷ 14 = 1 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 85 | 10880 |
| 74 and 157 | 11618 |
| 121 and 58 | 7018 |
| 135 and 104 | 14040 |
| 37 and 177 | 6549 |