Least Common Multiple (LCM) of 142 and 175
The least common multiple (LCM) of 142 and 175 is 24850.
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 175?
First, calculate the GCD of 142 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 175 = 0 remainder 142 |
| 2 | 175 ÷ 142 = 1 remainder 33 |
| 3 | 142 ÷ 33 = 4 remainder 10 |
| 4 | 33 ÷ 10 = 3 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 25 | 350 |
| 40 and 57 | 2280 |
| 173 and 32 | 5536 |
| 172 and 120 | 5160 |
| 198 and 58 | 5742 |