Least Common Multiple (LCM) of 77 and 175
The least common multiple (LCM) of 77 and 175 is 1925.
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 77 and 175?
First, calculate the GCD of 77 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 175 = 0 remainder 77 |
| 2 | 175 ÷ 77 = 2 remainder 21 |
| 3 | 77 ÷ 21 = 3 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 23 | 2714 |
| 58 and 104 | 3016 |
| 145 and 51 | 7395 |
| 67 and 159 | 10653 |
| 89 and 164 | 14596 |