Least Common Multiple (LCM) of 100 and 54
The least common multiple (LCM) of 100 and 54 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 100 and 54?
First, calculate the GCD of 100 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 54 = 1 remainder 46 |
| 2 | 54 ÷ 46 = 1 remainder 8 |
| 3 | 46 ÷ 8 = 5 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 104 | 6136 |
| 66 and 132 | 132 |
| 100 and 145 | 2900 |
| 197 and 142 | 27974 |
| 193 and 26 | 5018 |