Least Common Multiple (LCM) of 78 and 154
The least common multiple (LCM) of 78 and 154 is 6006.
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 154?
First, calculate the GCD of 78 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 154 = 0 remainder 78 |
| 2 | 154 ÷ 78 = 1 remainder 76 |
| 3 | 78 ÷ 76 = 1 remainder 2 |
| 4 | 76 ÷ 2 = 38 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 175 | 21350 |
| 55 and 75 | 825 |
| 198 and 105 | 6930 |
| 183 and 101 | 18483 |
| 135 and 73 | 9855 |