Least Common Multiple (LCM) of 101 and 180
The least common multiple (LCM) of 101 and 180 is 18180.
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 180?
First, calculate the GCD of 101 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 180 = 0 remainder 101 |
| 2 | 180 ÷ 101 = 1 remainder 79 |
| 3 | 101 ÷ 79 = 1 remainder 22 |
| 4 | 79 ÷ 22 = 3 remainder 13 |
| 5 | 22 ÷ 13 = 1 remainder 9 |
| 6 | 13 ÷ 9 = 1 remainder 4 |
| 7 | 9 ÷ 4 = 2 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 185 | 31080 |
| 55 and 111 | 6105 |
| 16 and 145 | 2320 |
| 111 and 141 | 5217 |
| 191 and 83 | 15853 |