Least Common Multiple (LCM) of 30 and 111
The least common multiple (LCM) of 30 and 111 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 30 and 111?
First, calculate the GCD of 30 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 111 = 0 remainder 30 |
| 2 | 111 ÷ 30 = 3 remainder 21 |
| 3 | 30 ÷ 21 = 1 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 180 | 3420 |
| 58 and 10 | 290 |
| 20 and 31 | 620 |
| 78 and 38 | 1482 |
| 139 and 143 | 19877 |