Least Common Multiple (LCM) of 65 and 72
The least common multiple (LCM) of 65 and 72 is 4680.
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 72?
First, calculate the GCD of 65 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 72 = 0 remainder 65 |
| 2 | 72 ÷ 65 = 1 remainder 7 |
| 3 | 65 ÷ 7 = 9 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 163 | 13855 |
| 149 and 43 | 6407 |
| 84 and 45 | 1260 |
| 166 and 123 | 20418 |
| 137 and 78 | 10686 |