Least Common Multiple (LCM) of 78 and 95
The least common multiple (LCM) of 78 and 95 is 7410.
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 78 and 95?
First, calculate the GCD of 78 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 95 = 0 remainder 78 |
| 2 | 95 ÷ 78 = 1 remainder 17 |
| 3 | 78 ÷ 17 = 4 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 96 | 3168 |
| 149 and 162 | 24138 |
| 190 and 167 | 31730 |
| 188 and 96 | 4512 |
| 126 and 130 | 8190 |