Least Common Multiple (LCM) of 54 and 39
The least common multiple (LCM) of 54 and 39 is 702.
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 39?
First, calculate the GCD of 54 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 39 = 1 remainder 15 |
| 2 | 39 ÷ 15 = 2 remainder 9 |
| 3 | 15 ÷ 9 = 1 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 155 | 15035 |
| 178 and 53 | 9434 |
| 140 and 56 | 280 |
| 83 and 50 | 4150 |
| 147 and 179 | 26313 |