Least Common Multiple (LCM) of 75 and 144
The least common multiple (LCM) of 75 and 144 is 3600.
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 144?
First, calculate the GCD of 75 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 144 = 0 remainder 75 |
| 2 | 144 ÷ 75 = 1 remainder 69 |
| 3 | 75 ÷ 69 = 1 remainder 6 |
| 4 | 69 ÷ 6 = 11 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 82 | 11234 |
| 69 and 138 | 138 |
| 67 and 157 | 10519 |
| 48 and 96 | 96 |
| 178 and 127 | 22606 |