Least Common Multiple (LCM) of 158 and 96
The least common multiple (LCM) of 158 and 96 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 158 and 96?
First, calculate the GCD of 158 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 158 ÷ 96 = 1 remainder 62 |
| 2 | 96 ÷ 62 = 1 remainder 34 |
| 3 | 62 ÷ 34 = 1 remainder 28 |
| 4 | 34 ÷ 28 = 1 remainder 6 |
| 5 | 28 ÷ 6 = 4 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 49 | 735 |
| 135 and 134 | 18090 |
| 53 and 109 | 5777 |
| 116 and 163 | 18908 |
| 33 and 186 | 2046 |