Least Common Multiple (LCM) of 115 and 142
The least common multiple (LCM) of 115 and 142 is 16330.
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 115 and 142?
First, calculate the GCD of 115 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 142 = 0 remainder 115 |
| 2 | 142 ÷ 115 = 1 remainder 27 |
| 3 | 115 ÷ 27 = 4 remainder 7 |
| 4 | 27 ÷ 7 = 3 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 198 | 4554 |
| 34 and 13 | 442 |
| 131 and 157 | 20567 |
| 18 and 97 | 1746 |
| 47 and 84 | 3948 |