Least Common Multiple (LCM) of 75 and 180
The least common multiple (LCM) of 75 and 180 is 900.
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 180?
First, calculate the GCD of 75 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 180 = 0 remainder 75 |
| 2 | 180 ÷ 75 = 2 remainder 30 |
| 3 | 75 ÷ 30 = 2 remainder 15 |
| 4 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 27 | 459 |
| 120 and 125 | 3000 |
| 153 and 49 | 7497 |
| 121 and 136 | 16456 |
| 71 and 117 | 8307 |