Least Common Multiple (LCM) of 30 and 45
The least common multiple (LCM) of 30 and 45 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 45?
First, calculate the GCD of 30 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 45 = 0 remainder 30 |
| 2 | 45 ÷ 30 = 1 remainder 15 |
| 3 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 101 | 14241 |
| 95 and 176 | 16720 |
| 82 and 88 | 3608 |
| 182 and 15 | 2730 |
| 192 and 80 | 960 |