Least Common Multiple (LCM) of 65 and 112
The least common multiple (LCM) of 65 and 112 is 7280.
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 112?
First, calculate the GCD of 65 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 112 = 0 remainder 65 |
| 2 | 112 ÷ 65 = 1 remainder 47 |
| 3 | 65 ÷ 47 = 1 remainder 18 |
| 4 | 47 ÷ 18 = 2 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 171 | 1710 |
| 97 and 80 | 7760 |
| 165 and 176 | 2640 |
| 12 and 24 | 24 |
| 103 and 101 | 10403 |