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 |
|---|---|
| 127 and 140 | 17780 |
| 62 and 99 | 6138 |
| 13 and 59 | 767 |
| 182 and 97 | 17654 |
| 198 and 193 | 38214 |