Least Common Multiple (LCM) of 107 and 142
The least common multiple (LCM) of 107 and 142 is 15194.
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 107 and 142?
First, calculate the GCD of 107 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 142 = 0 remainder 107 |
| 2 | 142 ÷ 107 = 1 remainder 35 |
| 3 | 107 ÷ 35 = 3 remainder 2 |
| 4 | 35 ÷ 2 = 17 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 13 | 130 |
| 35 and 67 | 2345 |
| 185 and 78 | 14430 |
| 47 and 178 | 8366 |
| 95 and 191 | 18145 |