Least Common Multiple (LCM) of 30 and 18
The least common multiple (LCM) of 30 and 18 is 90.
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 18?
First, calculate the GCD of 30 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 18 = 1 remainder 12 |
| 2 | 18 ÷ 12 = 1 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 119 | 13685 |
| 74 and 77 | 5698 |
| 32 and 75 | 2400 |
| 26 and 112 | 1456 |
| 165 and 75 | 825 |