Least Common Multiple (LCM) of 45 and 176
The least common multiple (LCM) of 45 and 176 is 7920.
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 45 and 176?
First, calculate the GCD of 45 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 176 = 0 remainder 45 |
| 2 | 176 ÷ 45 = 3 remainder 41 |
| 3 | 45 ÷ 41 = 1 remainder 4 |
| 4 | 41 ÷ 4 = 10 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 113 | 9153 |
| 78 and 46 | 1794 |
| 147 and 142 | 20874 |
| 158 and 15 | 2370 |
| 192 and 142 | 13632 |