Least Common Multiple (LCM) of 74 and 109
The least common multiple (LCM) of 74 and 109 is 8066.
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 109?
First, calculate the GCD of 74 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 109 = 0 remainder 74 |
| 2 | 109 ÷ 74 = 1 remainder 35 |
| 3 | 74 ÷ 35 = 2 remainder 4 |
| 4 | 35 ÷ 4 = 8 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 67 | 7236 |
| 194 and 18 | 1746 |
| 172 and 189 | 32508 |
| 186 and 14 | 1302 |
| 53 and 72 | 3816 |