Least Common Multiple (LCM) of 174 and 107
The least common multiple (LCM) of 174 and 107 is 18618.
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 174 and 107?
First, calculate the GCD of 174 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 107 = 1 remainder 67 |
| 2 | 107 ÷ 67 = 1 remainder 40 |
| 3 | 67 ÷ 40 = 1 remainder 27 |
| 4 | 40 ÷ 27 = 1 remainder 13 |
| 5 | 27 ÷ 13 = 2 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 54 | 3780 |
| 124 and 105 | 13020 |
| 180 and 180 | 180 |
| 54 and 128 | 3456 |
| 82 and 132 | 5412 |