Least Common Multiple (LCM) of 178 and 195
The least common multiple (LCM) of 178 and 195 is 34710.
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 195?
First, calculate the GCD of 178 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 195 = 0 remainder 178 |
| 2 | 195 ÷ 178 = 1 remainder 17 |
| 3 | 178 ÷ 17 = 10 remainder 8 |
| 4 | 17 ÷ 8 = 2 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 85 | 6630 |
| 16 and 150 | 1200 |
| 195 and 46 | 8970 |
| 115 and 30 | 690 |
| 51 and 105 | 1785 |