Least Common Multiple (LCM) of 177 and 40
The least common multiple (LCM) of 177 and 40 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 177 and 40?
First, calculate the GCD of 177 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 40 = 4 remainder 17 |
| 2 | 40 ÷ 17 = 2 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 57 | 2679 |
| 141 and 36 | 1692 |
| 108 and 76 | 2052 |
| 120 and 199 | 23880 |
| 120 and 88 | 1320 |