Least Common Multiple (LCM) of 111 and 174
The least common multiple (LCM) of 111 and 174 is 6438.
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 174?
First, calculate the GCD of 111 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 174 = 0 remainder 111 |
| 2 | 174 ÷ 111 = 1 remainder 63 |
| 3 | 111 ÷ 63 = 1 remainder 48 |
| 4 | 63 ÷ 48 = 1 remainder 15 |
| 5 | 48 ÷ 15 = 3 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 122 | 11346 |
| 109 and 36 | 3924 |
| 141 and 171 | 8037 |
| 85 and 105 | 1785 |
| 171 and 148 | 25308 |