Least Common Multiple (LCM) of 178 and 105
The least common multiple (LCM) of 178 and 105 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 178 and 105?
First, calculate the GCD of 178 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 105 = 1 remainder 73 |
| 2 | 105 ÷ 73 = 1 remainder 32 |
| 3 | 73 ÷ 32 = 2 remainder 9 |
| 4 | 32 ÷ 9 = 3 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 18 | 360 |
| 76 and 52 | 988 |
| 189 and 185 | 34965 |
| 187 and 36 | 6732 |
| 83 and 157 | 13031 |