Least Common Multiple (LCM) of 142 and 112
The least common multiple (LCM) of 142 and 112 is 7952.
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 112?
First, calculate the GCD of 142 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 112 = 1 remainder 30 |
| 2 | 112 ÷ 30 = 3 remainder 22 |
| 3 | 30 ÷ 22 = 1 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 51 | 1989 |
| 45 and 48 | 720 |
| 17 and 98 | 1666 |
| 101 and 130 | 13130 |
| 25 and 31 | 775 |