Least Common Multiple (LCM) of 45 and 178
The least common multiple (LCM) of 45 and 178 is 8010.
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 178?
First, calculate the GCD of 45 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 178 = 0 remainder 45 |
| 2 | 178 ÷ 45 = 3 remainder 43 |
| 3 | 45 ÷ 43 = 1 remainder 2 |
| 4 | 43 ÷ 2 = 21 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 68 | 3060 |
| 28 and 80 | 560 |
| 176 and 12 | 528 |
| 38 and 103 | 3914 |
| 80 and 54 | 2160 |