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 |
|---|---|
| 134 and 155 | 20770 |
| 187 and 45 | 8415 |
| 90 and 29 | 2610 |
| 105 and 51 | 1785 |
| 63 and 199 | 12537 |