Least Common Multiple (LCM) of 175 and 111
The least common multiple (LCM) of 175 and 111 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 175 and 111?
First, calculate the GCD of 175 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 111 = 1 remainder 64 |
| 2 | 111 ÷ 64 = 1 remainder 47 |
| 3 | 64 ÷ 47 = 1 remainder 17 |
| 4 | 47 ÷ 17 = 2 remainder 13 |
| 5 | 17 ÷ 13 = 1 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 113 | 1130 |
| 121 and 186 | 22506 |
| 54 and 83 | 4482 |
| 125 and 47 | 5875 |
| 102 and 112 | 5712 |