Least Common Multiple (LCM) of 23 and 158
The least common multiple (LCM) of 23 and 158 is 3634.
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 23 and 158?
First, calculate the GCD of 23 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 158 = 0 remainder 23 |
| 2 | 158 ÷ 23 = 6 remainder 20 |
| 3 | 23 ÷ 20 = 1 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 74 | 3034 |
| 40 and 135 | 1080 |
| 116 and 198 | 11484 |
| 112 and 91 | 1456 |
| 117 and 87 | 3393 |