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 |
|---|---|
| 171 and 119 | 20349 |
| 101 and 87 | 8787 |
| 188 and 63 | 11844 |
| 197 and 105 | 20685 |
| 94 and 44 | 2068 |