Least Common Multiple (LCM) of 175 and 126
The least common multiple (LCM) of 175 and 126 is 3150.
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 175 and 126?
First, calculate the GCD of 175 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 126 = 1 remainder 49 |
| 2 | 126 ÷ 49 = 2 remainder 28 |
| 3 | 49 ÷ 28 = 1 remainder 21 |
| 4 | 28 ÷ 21 = 1 remainder 7 |
| 5 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 174 | 2958 |
| 45 and 106 | 4770 |
| 28 and 46 | 644 |
| 125 and 198 | 24750 |
| 143 and 100 | 14300 |