Least Common Multiple (LCM) of 54 and 95
The least common multiple (LCM) of 54 and 95 is 5130.
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 95?
First, calculate the GCD of 54 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 95 = 0 remainder 54 |
| 2 | 95 ÷ 54 = 1 remainder 41 |
| 3 | 54 ÷ 41 = 1 remainder 13 |
| 4 | 41 ÷ 13 = 3 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 120 | 3480 |
| 85 and 98 | 8330 |
| 95 and 14 | 1330 |
| 49 and 85 | 4165 |
| 37 and 199 | 7363 |