Least Common Multiple (LCM) of 54 and 94
The least common multiple (LCM) of 54 and 94 is 2538.
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 94?
First, calculate the GCD of 54 and 94 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 94 = 0 remainder 54 |
| 2 | 94 ÷ 54 = 1 remainder 40 |
| 3 | 54 ÷ 40 = 1 remainder 14 |
| 4 | 40 ÷ 14 = 2 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 92 | 4140 |
| 169 and 94 | 15886 |
| 88 and 115 | 10120 |
| 135 and 142 | 19170 |
| 118 and 118 | 118 |