Least Common Multiple (LCM) of 69 and 175
The least common multiple (LCM) of 69 and 175 is 12075.
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 69 and 175?
First, calculate the GCD of 69 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 175 = 0 remainder 69 |
| 2 | 175 ÷ 69 = 2 remainder 37 |
| 3 | 69 ÷ 37 = 1 remainder 32 |
| 4 | 37 ÷ 32 = 1 remainder 5 |
| 5 | 32 ÷ 5 = 6 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 75 | 14775 |
| 77 and 27 | 2079 |
| 10 and 192 | 960 |
| 110 and 180 | 1980 |
| 112 and 69 | 7728 |