Least Common Multiple (LCM) of 105 and 142
The least common multiple (LCM) of 105 and 142 is 14910.
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 142?
First, calculate the GCD of 105 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 142 = 0 remainder 105 |
| 2 | 142 ÷ 105 = 1 remainder 37 |
| 3 | 105 ÷ 37 = 2 remainder 31 |
| 4 | 37 ÷ 31 = 1 remainder 6 |
| 5 | 31 ÷ 6 = 5 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 117 | 3744 |
| 135 and 60 | 540 |
| 75 and 86 | 6450 |
| 71 and 59 | 4189 |
| 189 and 125 | 23625 |