Least Common Multiple (LCM) of 114 and 65
The least common multiple (LCM) of 114 and 65 is 7410.
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 114 and 65?
First, calculate the GCD of 114 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 65 = 1 remainder 49 |
| 2 | 65 ÷ 49 = 1 remainder 16 |
| 3 | 49 ÷ 16 = 3 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 164 | 21484 |
| 54 and 157 | 8478 |
| 186 and 190 | 17670 |
| 83 and 109 | 9047 |
| 63 and 115 | 7245 |