Least Common Multiple (LCM) of 142 and 108
The least common multiple (LCM) of 142 and 108 is 7668.
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 142 and 108?
First, calculate the GCD of 142 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 108 = 1 remainder 34 |
| 2 | 108 ÷ 34 = 3 remainder 6 |
| 3 | 34 ÷ 6 = 5 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 43 | 4601 |
| 171 and 141 | 8037 |
| 32 and 28 | 224 |
| 20 and 71 | 1420 |
| 17 and 78 | 1326 |