Least Common Multiple (LCM) of 177 and 140
The least common multiple (LCM) of 177 and 140 is 24780.
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 140?
First, calculate the GCD of 177 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 140 = 1 remainder 37 |
| 2 | 140 ÷ 37 = 3 remainder 29 |
| 3 | 37 ÷ 29 = 1 remainder 8 |
| 4 | 29 ÷ 8 = 3 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 85 | 595 |
| 68 and 58 | 1972 |
| 38 and 151 | 5738 |
| 200 and 171 | 34200 |
| 33 and 75 | 825 |