Least Common Multiple (LCM) of 40 and 178
The least common multiple (LCM) of 40 and 178 is 3560.
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 40 and 178?
First, calculate the GCD of 40 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 178 = 0 remainder 40 |
| 2 | 178 ÷ 40 = 4 remainder 18 |
| 3 | 40 ÷ 18 = 2 remainder 4 |
| 4 | 18 ÷ 4 = 4 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 147 | 3234 |
| 145 and 127 | 18415 |
| 85 and 193 | 16405 |
| 181 and 100 | 18100 |
| 179 and 65 | 11635 |