Least Common Multiple (LCM) of 65 and 56
The least common multiple (LCM) of 65 and 56 is 3640.
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 56?
First, calculate the GCD of 65 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 56 = 1 remainder 9 |
| 2 | 56 ÷ 9 = 6 remainder 2 |
| 3 | 9 ÷ 2 = 4 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 86 | 8342 |
| 150 and 135 | 1350 |
| 53 and 30 | 1590 |
| 60 and 29 | 1740 |
| 175 and 116 | 20300 |