Least Common Multiple (LCM) of 105 and 158
The least common multiple (LCM) of 105 and 158 is 16590.
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 105 and 158?
First, calculate the GCD of 105 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 158 = 0 remainder 105 |
| 2 | 158 ÷ 105 = 1 remainder 53 |
| 3 | 105 ÷ 53 = 1 remainder 52 |
| 4 | 53 ÷ 52 = 1 remainder 1 |
| 5 | 52 ÷ 1 = 52 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 51 | 510 |
| 174 and 146 | 12702 |
| 85 and 75 | 1275 |
| 129 and 21 | 903 |
| 73 and 174 | 12702 |