Least Common Multiple (LCM) of 179 and 54
The least common multiple (LCM) of 179 and 54 is 9666.
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 179 and 54?
First, calculate the GCD of 179 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 54 = 3 remainder 17 |
| 2 | 54 ÷ 17 = 3 remainder 3 |
| 3 | 17 ÷ 3 = 5 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 118 | 10148 |
| 107 and 128 | 13696 |
| 126 and 55 | 6930 |
| 16 and 57 | 912 |
| 80 and 17 | 1360 |