Least Common Multiple (LCM) of 75 and 190
The least common multiple (LCM) of 75 and 190 is 2850.
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 75 and 190?
First, calculate the GCD of 75 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 190 = 0 remainder 75 |
| 2 | 190 ÷ 75 = 2 remainder 40 |
| 3 | 75 ÷ 40 = 1 remainder 35 |
| 4 | 40 ÷ 35 = 1 remainder 5 |
| 5 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 69 | 13800 |
| 102 and 153 | 306 |
| 42 and 86 | 1806 |
| 170 and 188 | 15980 |
| 155 and 160 | 4960 |