Least Common Multiple (LCM) of 111 and 179
The least common multiple (LCM) of 111 and 179 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 111 and 179?
First, calculate the GCD of 111 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 179 = 0 remainder 111 |
| 2 | 179 ÷ 111 = 1 remainder 68 |
| 3 | 111 ÷ 68 = 1 remainder 43 |
| 4 | 68 ÷ 43 = 1 remainder 25 |
| 5 | 43 ÷ 25 = 1 remainder 18 |
| 6 | 25 ÷ 18 = 1 remainder 7 |
| 7 | 18 ÷ 7 = 2 remainder 4 |
| 8 | 7 ÷ 4 = 1 remainder 3 |
| 9 | 4 ÷ 3 = 1 remainder 1 |
| 10 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 168 | 3360 |
| 92 and 19 | 1748 |
| 87 and 37 | 3219 |
| 129 and 16 | 2064 |
| 105 and 48 | 1680 |