Least Common Multiple (LCM) of 127 and 175
The least common multiple (LCM) of 127 and 175 is 22225.
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 127 and 175?
First, calculate the GCD of 127 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 175 = 0 remainder 127 |
| 2 | 175 ÷ 127 = 1 remainder 48 |
| 3 | 127 ÷ 48 = 2 remainder 31 |
| 4 | 48 ÷ 31 = 1 remainder 17 |
| 5 | 31 ÷ 17 = 1 remainder 14 |
| 6 | 17 ÷ 14 = 1 remainder 3 |
| 7 | 14 ÷ 3 = 4 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 121 | 12705 |
| 186 and 30 | 930 |
| 101 and 177 | 17877 |
| 123 and 188 | 23124 |
| 13 and 108 | 1404 |