Least Common Multiple (LCM) of 174 and 200
The least common multiple (LCM) of 174 and 200 is 17400.
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 200?
First, calculate the GCD of 174 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 200 = 0 remainder 174 |
| 2 | 200 ÷ 174 = 1 remainder 26 |
| 3 | 174 ÷ 26 = 6 remainder 18 |
| 4 | 26 ÷ 18 = 1 remainder 8 |
| 5 | 18 ÷ 8 = 2 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 175 | 2100 |
| 11 and 150 | 1650 |
| 88 and 48 | 528 |
| 103 and 90 | 9270 |
| 14 and 195 | 2730 |