Least Common Multiple (LCM) of 54 and 113
The least common multiple (LCM) of 54 and 113 is 6102.
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 113?
First, calculate the GCD of 54 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 113 = 0 remainder 54 |
| 2 | 113 ÷ 54 = 2 remainder 5 |
| 3 | 54 ÷ 5 = 10 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 51 | 1836 |
| 43 and 85 | 3655 |
| 55 and 180 | 1980 |
| 90 and 45 | 90 |
| 193 and 23 | 4439 |