Least Common Multiple (LCM) of 30 and 36
The least common multiple (LCM) of 30 and 36 is 180.
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 36?
First, calculate the GCD of 30 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 36 = 0 remainder 30 |
| 2 | 36 ÷ 30 = 1 remainder 6 |
| 3 | 30 ÷ 6 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 182 | 29666 |
| 144 and 80 | 720 |
| 37 and 190 | 7030 |
| 173 and 49 | 8477 |
| 184 and 120 | 2760 |