Least Common Multiple (LCM) of 45 and 190
The least common multiple (LCM) of 45 and 190 is 1710.
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 45 and 190?
First, calculate the GCD of 45 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 190 = 0 remainder 45 |
| 2 | 190 ÷ 45 = 4 remainder 10 |
| 3 | 45 ÷ 10 = 4 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 190 | 10070 |
| 106 and 40 | 2120 |
| 175 and 122 | 21350 |
| 106 and 42 | 2226 |
| 167 and 115 | 19205 |