Least Common Multiple (LCM) of 75 and 20
The least common multiple (LCM) of 75 and 20 is 300.
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 20?
First, calculate the GCD of 75 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 20 = 3 remainder 15 |
| 2 | 20 ÷ 15 = 1 remainder 5 |
| 3 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 85 | 14535 |
| 89 and 154 | 13706 |
| 136 and 143 | 19448 |
| 94 and 129 | 12126 |
| 90 and 162 | 810 |