Least Common Multiple (LCM) of 116 and 74
The least common multiple (LCM) of 116 and 74 is 4292.
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 74?
First, calculate the GCD of 116 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 74 = 1 remainder 42 |
| 2 | 74 ÷ 42 = 1 remainder 32 |
| 3 | 42 ÷ 32 = 1 remainder 10 |
| 4 | 32 ÷ 10 = 3 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 11 | 539 |
| 177 and 135 | 7965 |
| 191 and 76 | 14516 |
| 16 and 117 | 1872 |
| 113 and 123 | 13899 |