Least Common Multiple (LCM) of 65 and 108
The least common multiple (LCM) of 65 and 108 is 7020.
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 108?
First, calculate the GCD of 65 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 108 = 0 remainder 65 |
| 2 | 108 ÷ 65 = 1 remainder 43 |
| 3 | 65 ÷ 43 = 1 remainder 22 |
| 4 | 43 ÷ 22 = 1 remainder 21 |
| 5 | 22 ÷ 21 = 1 remainder 1 |
| 6 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 110 | 18590 |
| 121 and 84 | 10164 |
| 72 and 197 | 14184 |
| 77 and 113 | 8701 |
| 54 and 191 | 10314 |