Least Common Multiple (LCM) of 65 and 84
The least common multiple (LCM) of 65 and 84 is 5460.
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 84?
First, calculate the GCD of 65 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 84 = 0 remainder 65 |
| 2 | 84 ÷ 65 = 1 remainder 19 |
| 3 | 65 ÷ 19 = 3 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 38 | 1140 |
| 108 and 149 | 16092 |
| 149 and 190 | 28310 |
| 195 and 80 | 3120 |
| 165 and 161 | 26565 |