Least Common Multiple (LCM) of 75 and 60
The least common multiple (LCM) of 75 and 60 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 60?
First, calculate the GCD of 75 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 60 = 1 remainder 15 |
| 2 | 60 ÷ 15 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 110 | 330 |
| 104 and 176 | 2288 |
| 109 and 36 | 3924 |
| 178 and 41 | 7298 |
| 151 and 128 | 19328 |