Least Common Multiple (LCM) of 111 and 30
The least common multiple (LCM) of 111 and 30 is 1110.
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 30?
First, calculate the GCD of 111 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 30 = 3 remainder 21 |
| 2 | 30 ÷ 21 = 1 remainder 9 |
| 3 | 21 ÷ 9 = 2 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 42 | 5250 |
| 78 and 128 | 4992 |
| 154 and 71 | 10934 |
| 59 and 74 | 4366 |
| 100 and 97 | 9700 |