Least Common Multiple (LCM) of 105 and 179
The least common multiple (LCM) of 105 and 179 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 105 and 179?
First, calculate the GCD of 105 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 179 = 0 remainder 105 |
| 2 | 179 ÷ 105 = 1 remainder 74 |
| 3 | 105 ÷ 74 = 1 remainder 31 |
| 4 | 74 ÷ 31 = 2 remainder 12 |
| 5 | 31 ÷ 12 = 2 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 100 | 11300 |
| 165 and 119 | 19635 |
| 161 and 192 | 30912 |
| 180 and 69 | 4140 |
| 15 and 124 | 1860 |