Least Common Multiple (LCM) of 39 and 142
The least common multiple (LCM) of 39 and 142 is 5538.
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 39 and 142?
First, calculate the GCD of 39 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 142 = 0 remainder 39 |
| 2 | 142 ÷ 39 = 3 remainder 25 |
| 3 | 39 ÷ 25 = 1 remainder 14 |
| 4 | 25 ÷ 14 = 1 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 15 | 1965 |
| 143 and 17 | 2431 |
| 80 and 179 | 14320 |
| 12 and 102 | 204 |
| 162 and 173 | 28026 |