Least Common Multiple (LCM) of 116 and 69
The least common multiple (LCM) of 116 and 69 is 8004.
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 69?
First, calculate the GCD of 116 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 69 = 1 remainder 47 |
| 2 | 69 ÷ 47 = 1 remainder 22 |
| 3 | 47 ÷ 22 = 2 remainder 3 |
| 4 | 22 ÷ 3 = 7 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 152 | 3496 |
| 169 and 35 | 5915 |
| 113 and 196 | 22148 |
| 51 and 189 | 3213 |
| 195 and 99 | 6435 |