Least Common Multiple (LCM) of 101 and 179
The least common multiple (LCM) of 101 and 179 is 18079.
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 101 and 179?
First, calculate the GCD of 101 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 179 = 0 remainder 101 |
| 2 | 179 ÷ 101 = 1 remainder 78 |
| 3 | 101 ÷ 78 = 1 remainder 23 |
| 4 | 78 ÷ 23 = 3 remainder 9 |
| 5 | 23 ÷ 9 = 2 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 108 | 1188 |
| 20 and 165 | 660 |
| 31 and 173 | 5363 |
| 191 and 163 | 31133 |
| 123 and 198 | 8118 |