Least Common Multiple (LCM) of 75 and 45
The least common multiple (LCM) of 75 and 45 is 225.
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 45?
First, calculate the GCD of 75 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 45 = 1 remainder 30 |
| 2 | 45 ÷ 30 = 1 remainder 15 |
| 3 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 69 | 4416 |
| 178 and 187 | 33286 |
| 87 and 23 | 2001 |
| 159 and 186 | 9858 |
| 149 and 15 | 2235 |