Least Common Multiple (LCM) of 179 and 111
The least common multiple (LCM) of 179 and 111 is 19869.
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 111?
First, calculate the GCD of 179 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 111 = 1 remainder 68 |
| 2 | 111 ÷ 68 = 1 remainder 43 |
| 3 | 68 ÷ 43 = 1 remainder 25 |
| 4 | 43 ÷ 25 = 1 remainder 18 |
| 5 | 25 ÷ 18 = 1 remainder 7 |
| 6 | 18 ÷ 7 = 2 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 116 | 7308 |
| 155 and 109 | 16895 |
| 105 and 42 | 210 |
| 150 and 147 | 7350 |
| 116 and 140 | 4060 |