Least Common Multiple (LCM) of 30 and 32
The least common multiple (LCM) of 30 and 32 is 480.
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 32?
First, calculate the GCD of 30 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 32 = 0 remainder 30 |
| 2 | 32 ÷ 30 = 1 remainder 2 |
| 3 | 30 ÷ 2 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 118 | 21358 |
| 114 and 196 | 11172 |
| 123 and 176 | 21648 |
| 45 and 100 | 900 |
| 196 and 155 | 30380 |