Least Common Multiple (LCM) of 78 and 175
The least common multiple (LCM) of 78 and 175 is 13650.
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 175?
First, calculate the GCD of 78 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 175 = 0 remainder 78 |
| 2 | 175 ÷ 78 = 2 remainder 19 |
| 3 | 78 ÷ 19 = 4 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 106 | 16642 |
| 115 and 197 | 22655 |
| 99 and 88 | 792 |
| 165 and 48 | 2640 |
| 161 and 186 | 29946 |