Least Common Multiple (LCM) of 105 and 178
The least common multiple (LCM) of 105 and 178 is 18690.
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 105 and 178?
First, calculate the GCD of 105 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 178 = 0 remainder 105 |
| 2 | 178 ÷ 105 = 1 remainder 73 |
| 3 | 105 ÷ 73 = 1 remainder 32 |
| 4 | 73 ÷ 32 = 2 remainder 9 |
| 5 | 32 ÷ 9 = 3 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 51 | 3060 |
| 110 and 14 | 770 |
| 150 and 146 | 10950 |
| 76 and 89 | 6764 |
| 85 and 140 | 2380 |