Least Common Multiple (LCM) of 78 and 196
The least common multiple (LCM) of 78 and 196 is 7644.
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 196?
First, calculate the GCD of 78 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 196 = 0 remainder 78 |
| 2 | 196 ÷ 78 = 2 remainder 40 |
| 3 | 78 ÷ 40 = 1 remainder 38 |
| 4 | 40 ÷ 38 = 1 remainder 2 |
| 5 | 38 ÷ 2 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 42 | 42 |
| 73 and 133 | 9709 |
| 71 and 163 | 11573 |
| 174 and 170 | 14790 |
| 162 and 97 | 15714 |