Least Common Multiple (LCM) of 65 and 12
The least common multiple (LCM) of 65 and 12 is 780.
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 12?
First, calculate the GCD of 65 and 12 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 12 = 5 remainder 5 |
| 2 | 12 ÷ 5 = 2 remainder 2 |
| 3 | 5 ÷ 2 = 2 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 71 | 6603 |
| 72 and 46 | 1656 |
| 141 and 180 | 8460 |
| 197 and 160 | 31520 |
| 115 and 189 | 21735 |