Least Common Multiple (LCM) of 78 and 179
The least common multiple (LCM) of 78 and 179 is 13962.
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 179?
First, calculate the GCD of 78 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 179 = 0 remainder 78 |
| 2 | 179 ÷ 78 = 2 remainder 23 |
| 3 | 78 ÷ 23 = 3 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 47 | 4888 |
| 70 and 169 | 11830 |
| 149 and 195 | 29055 |
| 189 and 115 | 21735 |
| 127 and 75 | 9525 |