Least Common Multiple (LCM) of 54 and 67
The least common multiple (LCM) of 54 and 67 is 3618.
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 67?
First, calculate the GCD of 54 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 67 = 0 remainder 54 |
| 2 | 67 ÷ 54 = 1 remainder 13 |
| 3 | 54 ÷ 13 = 4 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 68 | 10268 |
| 83 and 173 | 14359 |
| 157 and 174 | 27318 |
| 135 and 158 | 21330 |
| 30 and 75 | 150 |