Least Common Multiple (LCM) of 142 and 178
The least common multiple (LCM) of 142 and 178 is 12638.
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 178?
First, calculate the GCD of 142 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 178 = 0 remainder 142 |
| 2 | 178 ÷ 142 = 1 remainder 36 |
| 3 | 142 ÷ 36 = 3 remainder 34 |
| 4 | 36 ÷ 34 = 1 remainder 2 |
| 5 | 34 ÷ 2 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 25 | 3225 |
| 25 and 58 | 1450 |
| 65 and 12 | 780 |
| 108 and 52 | 1404 |
| 16 and 100 | 400 |