Least Common Multiple (LCM) of 32 and 142
The least common multiple (LCM) of 32 and 142 is 2272.
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 32 and 142?
First, calculate the GCD of 32 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 142 = 0 remainder 32 |
| 2 | 142 ÷ 32 = 4 remainder 14 |
| 3 | 32 ÷ 14 = 2 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 30 | 1020 |
| 139 and 32 | 4448 |
| 32 and 180 | 1440 |
| 126 and 52 | 3276 |
| 56 and 110 | 3080 |