Least Common Multiple (LCM) of 126 and 175
The least common multiple (LCM) of 126 and 175 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 126 and 175?
First, calculate the GCD of 126 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 175 = 0 remainder 126 |
| 2 | 175 ÷ 126 = 1 remainder 49 |
| 3 | 126 ÷ 49 = 2 remainder 28 |
| 4 | 49 ÷ 28 = 1 remainder 21 |
| 5 | 28 ÷ 21 = 1 remainder 7 |
| 6 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 16 | 720 |
| 45 and 138 | 2070 |
| 154 and 22 | 154 |
| 37 and 120 | 4440 |
| 78 and 170 | 6630 |