Least Common Multiple (LCM) of 65 and 87
The least common multiple (LCM) of 65 and 87 is 5655.
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 87?
First, calculate the GCD of 65 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 87 = 0 remainder 65 |
| 2 | 87 ÷ 65 = 1 remainder 22 |
| 3 | 65 ÷ 22 = 2 remainder 21 |
| 4 | 22 ÷ 21 = 1 remainder 1 |
| 5 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 122 | 1830 |
| 70 and 66 | 2310 |
| 94 and 37 | 3478 |
| 131 and 75 | 9825 |
| 172 and 31 | 5332 |