Least Common Multiple (LCM) of 196 and 54
The least common multiple (LCM) of 196 and 54 is 5292.
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 196 and 54?
First, calculate the GCD of 196 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 54 = 3 remainder 34 |
| 2 | 54 ÷ 34 = 1 remainder 20 |
| 3 | 34 ÷ 20 = 1 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 109 | 6213 |
| 194 and 103 | 19982 |
| 95 and 16 | 1520 |
| 163 and 47 | 7661 |
| 45 and 90 | 90 |