Least Common Multiple (LCM) of 142 and 30
The least common multiple (LCM) of 142 and 30 is 2130.
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 30?
First, calculate the GCD of 142 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 30 = 4 remainder 22 |
| 2 | 30 ÷ 22 = 1 remainder 8 |
| 3 | 22 ÷ 8 = 2 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 146 | 15914 |
| 80 and 110 | 880 |
| 173 and 135 | 23355 |
| 75 and 123 | 3075 |
| 77 and 47 | 3619 |