Least Common Multiple (LCM) of 67 and 142
The least common multiple (LCM) of 67 and 142 is 9514.
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 67 and 142?
First, calculate the GCD of 67 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 142 = 0 remainder 67 |
| 2 | 142 ÷ 67 = 2 remainder 8 |
| 3 | 67 ÷ 8 = 8 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 121 | 16214 |
| 14 and 20 | 140 |
| 173 and 100 | 17300 |
| 31 and 43 | 1333 |
| 10 and 190 | 190 |