Least Common Multiple (LCM) of 54 and 100
The least common multiple (LCM) of 54 and 100 is 2700.
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 100?
First, calculate the GCD of 54 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 100 = 0 remainder 54 |
| 2 | 100 ÷ 54 = 1 remainder 46 |
| 3 | 54 ÷ 46 = 1 remainder 8 |
| 4 | 46 ÷ 8 = 5 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 144 | 720 |
| 118 and 104 | 6136 |
| 145 and 19 | 2755 |
| 83 and 27 | 2241 |
| 182 and 19 | 3458 |