Least Common Multiple (LCM) of 74 and 190
The least common multiple (LCM) of 74 and 190 is 7030.
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 190?
First, calculate the GCD of 74 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 190 = 0 remainder 74 |
| 2 | 190 ÷ 74 = 2 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 |
|---|---|
| 117 and 54 | 702 |
| 60 and 179 | 10740 |
| 17 and 177 | 3009 |
| 90 and 30 | 90 |
| 136 and 117 | 15912 |