Least Common Multiple (LCM) of 97 and 54
The least common multiple (LCM) of 97 and 54 is 5238.
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 97 and 54?
First, calculate the GCD of 97 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 54 = 1 remainder 43 |
| 2 | 54 ÷ 43 = 1 remainder 11 |
| 3 | 43 ÷ 11 = 3 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 34 | 5542 |
| 108 and 179 | 19332 |
| 101 and 14 | 1414 |
| 62 and 169 | 10478 |
| 131 and 105 | 13755 |