Least Common Multiple (LCM) of 108 and 142
The least common multiple (LCM) of 108 and 142 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 108 and 142?
First, calculate the GCD of 108 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 142 = 0 remainder 108 |
| 2 | 142 ÷ 108 = 1 remainder 34 |
| 3 | 108 ÷ 34 = 3 remainder 6 |
| 4 | 34 ÷ 6 = 5 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 90 | 450 |
| 161 and 78 | 12558 |
| 45 and 40 | 360 |
| 187 and 31 | 5797 |
| 40 and 172 | 1720 |