Least Common Multiple (LCM) of 178 and 45
The least common multiple (LCM) of 178 and 45 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 178 and 45?
First, calculate the GCD of 178 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 45 = 3 remainder 43 |
| 2 | 45 ÷ 43 = 1 remainder 2 |
| 3 | 43 ÷ 2 = 21 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 134 | 17018 |
| 61 and 159 | 9699 |
| 111 and 22 | 2442 |
| 65 and 76 | 4940 |
| 172 and 53 | 9116 |