Least Common Multiple (LCM) of 105 and 174
The least common multiple (LCM) of 105 and 174 is 6090.
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 105 and 174?
First, calculate the GCD of 105 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 174 = 0 remainder 105 |
| 2 | 174 ÷ 105 = 1 remainder 69 |
| 3 | 105 ÷ 69 = 1 remainder 36 |
| 4 | 69 ÷ 36 = 1 remainder 33 |
| 5 | 36 ÷ 33 = 1 remainder 3 |
| 6 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 56 | 2408 |
| 19 and 198 | 3762 |
| 161 and 89 | 14329 |
| 61 and 177 | 10797 |
| 120 and 153 | 6120 |