Least Common Multiple (LCM) of 78 and 176
The least common multiple (LCM) of 78 and 176 is 6864.
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 176?
First, calculate the GCD of 78 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 176 = 0 remainder 78 |
| 2 | 176 ÷ 78 = 2 remainder 20 |
| 3 | 78 ÷ 20 = 3 remainder 18 |
| 4 | 20 ÷ 18 = 1 remainder 2 |
| 5 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 114 | 6726 |
| 52 and 129 | 6708 |
| 76 and 171 | 684 |
| 138 and 43 | 5934 |
| 40 and 189 | 7560 |