Least Common Multiple (LCM) of 36 and 54
The least common multiple (LCM) of 36 and 54 is 108.
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 36 and 54?
First, calculate the GCD of 36 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 54 = 0 remainder 36 |
| 2 | 54 ÷ 36 = 1 remainder 18 |
| 3 | 36 ÷ 18 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 180 | 1260 |
| 137 and 49 | 6713 |
| 59 and 54 | 3186 |
| 101 and 139 | 14039 |
| 127 and 129 | 16383 |