Least Common Multiple (LCM) of 72 and 75
The least common multiple (LCM) of 72 and 75 is 1800.
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 72 and 75?
First, calculate the GCD of 72 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 75 = 0 remainder 72 |
| 2 | 75 ÷ 72 = 1 remainder 3 |
| 3 | 72 ÷ 3 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 65 | 6240 |
| 189 and 42 | 378 |
| 150 and 50 | 150 |
| 195 and 24 | 1560 |
| 90 and 36 | 180 |