Least Common Multiple (LCM) of 54 and 133
The least common multiple (LCM) of 54 and 133 is 7182.
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 133?
First, calculate the GCD of 54 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 133 = 0 remainder 54 |
| 2 | 133 ÷ 54 = 2 remainder 25 |
| 3 | 54 ÷ 25 = 2 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 158 | 1264 |
| 68 and 99 | 6732 |
| 142 and 197 | 27974 |
| 189 and 40 | 7560 |
| 161 and 158 | 25438 |