Least Common Multiple (LCM) of 30 and 39
The least common multiple (LCM) of 30 and 39 is 390.
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 39?
First, calculate the GCD of 30 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 39 = 0 remainder 30 |
| 2 | 39 ÷ 30 = 1 remainder 9 |
| 3 | 30 ÷ 9 = 3 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 170 | 3740 |
| 101 and 18 | 1818 |
| 186 and 20 | 1860 |
| 198 and 12 | 396 |
| 102 and 147 | 4998 |