Least Common Multiple (LCM) of 68 and 175
The least common multiple (LCM) of 68 and 175 is 11900.
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 68 and 175?
First, calculate the GCD of 68 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 175 = 0 remainder 68 |
| 2 | 175 ÷ 68 = 2 remainder 39 |
| 3 | 68 ÷ 39 = 1 remainder 29 |
| 4 | 39 ÷ 29 = 1 remainder 10 |
| 5 | 29 ÷ 10 = 2 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 75 | 600 |
| 56 and 163 | 9128 |
| 24 and 51 | 408 |
| 137 and 30 | 4110 |
| 65 and 85 | 1105 |