Least Common Multiple (LCM) of 111 and 175
The least common multiple (LCM) of 111 and 175 is 19425.
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 111 and 175?
First, calculate the GCD of 111 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 175 = 0 remainder 111 |
| 2 | 175 ÷ 111 = 1 remainder 64 |
| 3 | 111 ÷ 64 = 1 remainder 47 |
| 4 | 64 ÷ 47 = 1 remainder 17 |
| 5 | 47 ÷ 17 = 2 remainder 13 |
| 6 | 17 ÷ 13 = 1 remainder 4 |
| 7 | 13 ÷ 4 = 3 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 128 | 19584 |
| 70 and 40 | 280 |
| 130 and 58 | 3770 |
| 18 and 142 | 1278 |
| 26 and 36 | 468 |