Least Common Multiple (LCM) of 114 and 175
The least common multiple (LCM) of 114 and 175 is 19950.
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 114 and 175?
First, calculate the GCD of 114 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 175 = 0 remainder 114 |
| 2 | 175 ÷ 114 = 1 remainder 61 |
| 3 | 114 ÷ 61 = 1 remainder 53 |
| 4 | 61 ÷ 53 = 1 remainder 8 |
| 5 | 53 ÷ 8 = 6 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 125 | 2625 |
| 150 and 32 | 2400 |
| 67 and 187 | 12529 |
| 132 and 119 | 15708 |
| 26 and 29 | 754 |