Least Common Multiple (LCM) of 43 and 177
The least common multiple (LCM) of 43 and 177 is 7611.
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 177?
First, calculate the GCD of 43 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 177 = 0 remainder 43 |
| 2 | 177 ÷ 43 = 4 remainder 5 |
| 3 | 43 ÷ 5 = 8 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 26 | 1586 |
| 137 and 108 | 14796 |
| 123 and 143 | 17589 |
| 10 and 21 | 210 |
| 21 and 153 | 1071 |