Least Common Multiple (LCM) of 42 and 143
The least common multiple (LCM) of 42 and 143 is 6006.
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 42 and 143?
First, calculate the GCD of 42 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 143 = 0 remainder 42 |
| 2 | 143 ÷ 42 = 3 remainder 17 |
| 3 | 42 ÷ 17 = 2 remainder 8 |
| 4 | 17 ÷ 8 = 2 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 120 | 23160 |
| 140 and 162 | 11340 |
| 144 and 42 | 1008 |
| 140 and 118 | 8260 |
| 146 and 97 | 14162 |