Least Common Multiple (LCM) of 65 and 59
The least common multiple (LCM) of 65 and 59 is 3835.
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 59?
First, calculate the GCD of 65 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 59 = 1 remainder 6 |
| 2 | 59 ÷ 6 = 9 remainder 5 |
| 3 | 6 ÷ 5 = 1 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 57 | 171 |
| 181 and 110 | 19910 |
| 137 and 141 | 19317 |
| 173 and 128 | 22144 |
| 49 and 198 | 9702 |