Least Common Multiple (LCM) of 65 and 89
The least common multiple (LCM) of 65 and 89 is 5785.
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 89?
First, calculate the GCD of 65 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 89 = 0 remainder 65 |
| 2 | 89 ÷ 65 = 1 remainder 24 |
| 3 | 65 ÷ 24 = 2 remainder 17 |
| 4 | 24 ÷ 17 = 1 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 100 | 2100 |
| 17 and 139 | 2363 |
| 37 and 70 | 2590 |
| 22 and 42 | 462 |
| 121 and 82 | 9922 |