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 |
|---|---|
| 105 and 54 | 1890 |
| 184 and 162 | 14904 |
| 128 and 154 | 9856 |
| 125 and 178 | 22250 |
| 123 and 156 | 6396 |