Least Common Multiple (LCM) of 65 and 37
The least common multiple (LCM) of 65 and 37 is 2405.
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 37?
First, calculate the GCD of 65 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 37 = 1 remainder 28 |
| 2 | 37 ÷ 28 = 1 remainder 9 |
| 3 | 28 ÷ 9 = 3 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 169 | 28223 |
| 136 and 169 | 22984 |
| 27 and 109 | 2943 |
| 112 and 100 | 2800 |
| 66 and 39 | 858 |