Least Common Multiple (LCM) of 56 and 65
The least common multiple (LCM) of 56 and 65 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 56 and 65?
First, calculate the GCD of 56 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 65 = 0 remainder 56 |
| 2 | 65 ÷ 56 = 1 remainder 9 |
| 3 | 56 ÷ 9 = 6 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 157 | 24021 |
| 102 and 55 | 5610 |
| 32 and 59 | 1888 |
| 137 and 25 | 3425 |
| 125 and 28 | 3500 |