Least Common Multiple (LCM) of 174 and 49
The least common multiple (LCM) of 174 and 49 is 8526.
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 49?
First, calculate the GCD of 174 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 49 = 3 remainder 27 |
| 2 | 49 ÷ 27 = 1 remainder 22 |
| 3 | 27 ÷ 22 = 1 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 59 | 10797 |
| 127 and 67 | 8509 |
| 60 and 82 | 2460 |
| 56 and 176 | 1232 |
| 189 and 95 | 17955 |