Least Common Multiple (LCM) of 30 and 13
The least common multiple (LCM) of 30 and 13 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 13?
First, calculate the GCD of 30 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 13 = 2 remainder 4 |
| 2 | 13 ÷ 4 = 3 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 29 | 4843 |
| 80 and 45 | 720 |
| 136 and 89 | 12104 |
| 95 and 70 | 1330 |
| 11 and 184 | 2024 |