Least Common Multiple (LCM) of 76 and 175
The least common multiple (LCM) of 76 and 175 is 13300.
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 76 and 175?
First, calculate the GCD of 76 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 175 = 0 remainder 76 |
| 2 | 175 ÷ 76 = 2 remainder 23 |
| 3 | 76 ÷ 23 = 3 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 198 | 13860 |
| 121 and 200 | 24200 |
| 114 and 188 | 10716 |
| 68 and 90 | 3060 |
| 86 and 129 | 258 |