Least Common Multiple (LCM) of 74 and 116
The least common multiple (LCM) of 74 and 116 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 74 and 116?
First, calculate the GCD of 74 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 116 = 0 remainder 74 |
| 2 | 116 ÷ 74 = 1 remainder 42 |
| 3 | 74 ÷ 42 = 1 remainder 32 |
| 4 | 42 ÷ 32 = 1 remainder 10 |
| 5 | 32 ÷ 10 = 3 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 66 | 1122 |
| 74 and 199 | 14726 |
| 194 and 172 | 16684 |
| 120 and 75 | 600 |
| 149 and 71 | 10579 |