Least Common Multiple (LCM) of 97 and 78
The least common multiple (LCM) of 97 and 78 is 7566.
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 78?
First, calculate the GCD of 97 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 78 = 1 remainder 19 |
| 2 | 78 ÷ 19 = 4 remainder 2 |
| 3 | 19 ÷ 2 = 9 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 182 | 24934 |
| 44 and 103 | 4532 |
| 67 and 134 | 134 |
| 100 and 189 | 18900 |
| 162 and 79 | 12798 |