Least Common Multiple (LCM) of 109 and 174
The least common multiple (LCM) of 109 and 174 is 18966.
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 109 and 174?
First, calculate the GCD of 109 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 174 = 0 remainder 109 |
| 2 | 174 ÷ 109 = 1 remainder 65 |
| 3 | 109 ÷ 65 = 1 remainder 44 |
| 4 | 65 ÷ 44 = 1 remainder 21 |
| 5 | 44 ÷ 21 = 2 remainder 2 |
| 6 | 21 ÷ 2 = 10 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 103 | 12566 |
| 104 and 92 | 2392 |
| 46 and 97 | 4462 |
| 155 and 172 | 26660 |
| 200 and 62 | 6200 |