Least Common Multiple (LCM) of 111 and 130
The least common multiple (LCM) of 111 and 130 is 14430.
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 130?
First, calculate the GCD of 111 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 130 = 0 remainder 111 |
| 2 | 130 ÷ 111 = 1 remainder 19 |
| 3 | 111 ÷ 19 = 5 remainder 16 |
| 4 | 19 ÷ 16 = 1 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 60 | 1380 |
| 88 and 200 | 2200 |
| 55 and 45 | 495 |
| 102 and 188 | 9588 |
| 188 and 169 | 31772 |