Least Common Multiple (LCM) of 45 and 96
The least common multiple (LCM) of 45 and 96 is 1440.
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 45 and 96?
First, calculate the GCD of 45 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 96 = 0 remainder 45 |
| 2 | 96 ÷ 45 = 2 remainder 6 |
| 3 | 45 ÷ 6 = 7 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 108 | 1080 |
| 81 and 92 | 7452 |
| 171 and 22 | 3762 |
| 133 and 102 | 13566 |
| 173 and 178 | 30794 |