Least Common Multiple (LCM) of 30 and 24
The least common multiple (LCM) of 30 and 24 is 120.
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 24?
First, calculate the GCD of 30 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 24 = 1 remainder 6 |
| 2 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 17 | 1275 |
| 187 and 142 | 26554 |
| 180 and 198 | 1980 |
| 12 and 14 | 84 |
| 104 and 24 | 312 |