Least Common Multiple (LCM) of 179 and 105
The least common multiple (LCM) of 179 and 105 is 18795.
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 179 and 105?
First, calculate the GCD of 179 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 105 = 1 remainder 74 |
| 2 | 105 ÷ 74 = 1 remainder 31 |
| 3 | 74 ÷ 31 = 2 remainder 12 |
| 4 | 31 ÷ 12 = 2 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 194 | 4462 |
| 90 and 34 | 1530 |
| 60 and 75 | 300 |
| 110 and 180 | 1980 |
| 17 and 100 | 1700 |