Least Common Multiple (LCM) of 178 and 66
The least common multiple (LCM) of 178 and 66 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 178 and 66?
First, calculate the GCD of 178 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 66 = 2 remainder 46 |
| 2 | 66 ÷ 46 = 1 remainder 20 |
| 3 | 46 ÷ 20 = 2 remainder 6 |
| 4 | 20 ÷ 6 = 3 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 87 | 870 |
| 75 and 170 | 2550 |
| 16 and 70 | 560 |
| 171 and 24 | 1368 |
| 65 and 42 | 2730 |