Least Common Multiple (LCM) of 54 and 76
The least common multiple (LCM) of 54 and 76 is 2052.
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 76?
First, calculate the GCD of 54 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 76 = 0 remainder 54 |
| 2 | 76 ÷ 54 = 1 remainder 22 |
| 3 | 54 ÷ 22 = 2 remainder 10 |
| 4 | 22 ÷ 10 = 2 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 128 | 128 |
| 113 and 108 | 12204 |
| 73 and 178 | 12994 |
| 168 and 45 | 2520 |
| 192 and 21 | 1344 |