Least Common Multiple (LCM) of 54 and 72
The least common multiple (LCM) of 54 and 72 is 216.
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 54 and 72?
First, calculate the GCD of 54 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 72 = 0 remainder 54 |
| 2 | 72 ÷ 54 = 1 remainder 18 |
| 3 | 54 ÷ 18 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 116 | 21692 |
| 157 and 84 | 13188 |
| 78 and 97 | 7566 |
| 20 and 186 | 1860 |
| 113 and 175 | 19775 |