Least Common Multiple (LCM) of 165 and 178
The least common multiple (LCM) of 165 and 178 is 29370.
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 165 and 178?
First, calculate the GCD of 165 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 178 = 0 remainder 165 |
| 2 | 178 ÷ 165 = 1 remainder 13 |
| 3 | 165 ÷ 13 = 12 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 90 | 8730 |
| 71 and 143 | 10153 |
| 189 and 64 | 12096 |
| 95 and 152 | 760 |
| 101 and 183 | 18483 |