Least Common Multiple (LCM) of 43 and 178
The least common multiple (LCM) of 43 and 178 is 7654.
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 43 and 178?
First, calculate the GCD of 43 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 178 = 0 remainder 43 |
| 2 | 178 ÷ 43 = 4 remainder 6 |
| 3 | 43 ÷ 6 = 7 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 81 | 10125 |
| 200 and 182 | 18200 |
| 49 and 67 | 3283 |
| 111 and 87 | 3219 |
| 119 and 94 | 11186 |