Least Common Multiple (LCM) of 65 and 36
The least common multiple (LCM) of 65 and 36 is 2340.
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 36?
First, calculate the GCD of 65 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 36 = 1 remainder 29 |
| 2 | 36 ÷ 29 = 1 remainder 7 |
| 3 | 29 ÷ 7 = 4 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 11 | 880 |
| 178 and 155 | 27590 |
| 97 and 72 | 6984 |
| 26 and 127 | 3302 |
| 89 and 49 | 4361 |