Least Common Multiple (LCM) of 116 and 65
The least common multiple (LCM) of 116 and 65 is 7540.
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 116 and 65?
First, calculate the GCD of 116 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 65 = 1 remainder 51 |
| 2 | 65 ÷ 51 = 1 remainder 14 |
| 3 | 51 ÷ 14 = 3 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 43 | 4257 |
| 189 and 63 | 189 |
| 37 and 196 | 7252 |
| 168 and 38 | 3192 |
| 135 and 47 | 6345 |