Least Common Multiple (LCM) of 40 and 177
The least common multiple (LCM) of 40 and 177 is 7080.
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 177?
First, calculate the GCD of 40 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 177 = 0 remainder 40 |
| 2 | 177 ÷ 40 = 4 remainder 17 |
| 3 | 40 ÷ 17 = 2 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 75 | 2550 |
| 75 and 165 | 825 |
| 160 and 165 | 5280 |
| 67 and 164 | 10988 |
| 111 and 104 | 11544 |