Least Common Multiple (LCM) of 174 and 100
The least common multiple (LCM) of 174 and 100 is 8700.
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 100?
First, calculate the GCD of 174 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 100 = 1 remainder 74 |
| 2 | 100 ÷ 74 = 1 remainder 26 |
| 3 | 74 ÷ 26 = 2 remainder 22 |
| 4 | 26 ÷ 22 = 1 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 141 | 15087 |
| 192 and 76 | 3648 |
| 46 and 199 | 9154 |
| 184 and 110 | 10120 |
| 19 and 86 | 1634 |