Least Common Multiple (LCM) of 43 and 142
The least common multiple (LCM) of 43 and 142 is 6106.
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 43 and 142?
First, calculate the GCD of 43 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 142 = 0 remainder 43 |
| 2 | 142 ÷ 43 = 3 remainder 13 |
| 3 | 43 ÷ 13 = 3 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 75 | 525 |
| 132 and 79 | 10428 |
| 177 and 138 | 8142 |
| 185 and 164 | 30340 |
| 49 and 38 | 1862 |