Least Common Multiple (LCM) of 96 and 145
The least common multiple (LCM) of 96 and 145 is 13920.
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 96 and 145?
First, calculate the GCD of 96 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 145 = 0 remainder 96 |
| 2 | 145 ÷ 96 = 1 remainder 49 |
| 3 | 96 ÷ 49 = 1 remainder 47 |
| 4 | 49 ÷ 47 = 1 remainder 2 |
| 5 | 47 ÷ 2 = 23 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 46 | 2070 |
| 157 and 173 | 27161 |
| 192 and 150 | 4800 |
| 86 and 94 | 4042 |
| 31 and 123 | 3813 |