Least Common Multiple (LCM) of 96 and 158
The least common multiple (LCM) of 96 and 158 is 7584.
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 158?
First, calculate the GCD of 96 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 158 = 0 remainder 96 |
| 2 | 158 ÷ 96 = 1 remainder 62 |
| 3 | 96 ÷ 62 = 1 remainder 34 |
| 4 | 62 ÷ 34 = 1 remainder 28 |
| 5 | 34 ÷ 28 = 1 remainder 6 |
| 6 | 28 ÷ 6 = 4 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 105 | 1680 |
| 180 and 159 | 9540 |
| 11 and 92 | 1012 |
| 185 and 156 | 28860 |
| 53 and 18 | 954 |