Least Common Multiple (LCM) of 66 and 178
The least common multiple (LCM) of 66 and 178 is 5874.
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 66 and 178?
First, calculate the GCD of 66 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 178 = 0 remainder 66 |
| 2 | 178 ÷ 66 = 2 remainder 46 |
| 3 | 66 ÷ 46 = 1 remainder 20 |
| 4 | 46 ÷ 20 = 2 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 73 | 10293 |
| 20 and 112 | 560 |
| 110 and 163 | 17930 |
| 20 and 36 | 180 |
| 177 and 194 | 34338 |