Least Common Multiple (LCM) of 75 and 72
The least common multiple (LCM) of 75 and 72 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 75 and 72?
First, calculate the GCD of 75 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 72 = 1 remainder 3 |
| 2 | 72 ÷ 3 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 121 | 17545 |
| 191 and 96 | 18336 |
| 152 and 34 | 2584 |
| 52 and 10 | 260 |
| 114 and 29 | 3306 |