Least Common Multiple (LCM) of 54 and 91
The least common multiple (LCM) of 54 and 91 is 4914.
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 91?
First, calculate the GCD of 54 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 91 = 0 remainder 54 |
| 2 | 91 ÷ 54 = 1 remainder 37 |
| 3 | 54 ÷ 37 = 1 remainder 17 |
| 4 | 37 ÷ 17 = 2 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 107 | 13696 |
| 142 and 111 | 15762 |
| 190 and 162 | 15390 |
| 39 and 105 | 1365 |
| 73 and 73 | 73 |