Least Common Multiple (LCM) of 78 and 172
The least common multiple (LCM) of 78 and 172 is 6708.
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 172?
First, calculate the GCD of 78 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 172 = 0 remainder 78 |
| 2 | 172 ÷ 78 = 2 remainder 16 |
| 3 | 78 ÷ 16 = 4 remainder 14 |
| 4 | 16 ÷ 14 = 1 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 191 | 23493 |
| 138 and 86 | 5934 |
| 115 and 167 | 19205 |
| 109 and 65 | 7085 |
| 48 and 167 | 8016 |