Least Common Multiple (LCM) of 12 and 30
The least common multiple (LCM) of 12 and 30 is 60.
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 12 and 30?
First, calculate the GCD of 12 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 30 = 0 remainder 12 |
| 2 | 30 ÷ 12 = 2 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 189 | 945 |
| 188 and 28 | 1316 |
| 29 and 146 | 4234 |
| 160 and 105 | 3360 |
| 109 and 145 | 15805 |