Least Common Multiple (LCM) of 175 and 114
The least common multiple (LCM) of 175 and 114 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 175 and 114?
First, calculate the GCD of 175 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 114 = 1 remainder 61 |
| 2 | 114 ÷ 61 = 1 remainder 53 |
| 3 | 61 ÷ 53 = 1 remainder 8 |
| 4 | 53 ÷ 8 = 6 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 30 | 2220 |
| 114 and 105 | 3990 |
| 43 and 138 | 5934 |
| 67 and 198 | 13266 |
| 18 and 51 | 306 |