Least Common Multiple (LCM) of 74 and 195
The least common multiple (LCM) of 74 and 195 is 14430.
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 195?
First, calculate the GCD of 74 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 195 = 0 remainder 74 |
| 2 | 195 ÷ 74 = 2 remainder 47 |
| 3 | 74 ÷ 47 = 1 remainder 27 |
| 4 | 47 ÷ 27 = 1 remainder 20 |
| 5 | 27 ÷ 20 = 1 remainder 7 |
| 6 | 20 ÷ 7 = 2 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 72 | 144 |
| 130 and 144 | 9360 |
| 81 and 17 | 1377 |
| 49 and 155 | 7595 |
| 174 and 158 | 13746 |