Least Common Multiple (LCM) of 75 and 96
The least common multiple (LCM) of 75 and 96 is 2400.
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 96?
First, calculate the GCD of 75 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 96 = 0 remainder 75 |
| 2 | 96 ÷ 75 = 1 remainder 21 |
| 3 | 75 ÷ 21 = 3 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 140 | 1540 |
| 169 and 81 | 13689 |
| 134 and 136 | 9112 |
| 20 and 106 | 1060 |
| 137 and 174 | 23838 |