Least Common Multiple (LCM) of 42 and 178
The least common multiple (LCM) of 42 and 178 is 3738.
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 42 and 178?
First, calculate the GCD of 42 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 178 = 0 remainder 42 |
| 2 | 178 ÷ 42 = 4 remainder 10 |
| 3 | 42 ÷ 10 = 4 remainder 2 |
| 4 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 78 | 4290 |
| 28 and 42 | 84 |
| 100 and 31 | 3100 |
| 144 and 191 | 27504 |
| 50 and 17 | 850 |