Least Common Multiple (LCM) of 49 and 174
The least common multiple (LCM) of 49 and 174 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 49 and 174?
First, calculate the GCD of 49 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 174 = 0 remainder 49 |
| 2 | 174 ÷ 49 = 3 remainder 27 |
| 3 | 49 ÷ 27 = 1 remainder 22 |
| 4 | 27 ÷ 22 = 1 remainder 5 |
| 5 | 22 ÷ 5 = 4 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 124 | 3348 |
| 113 and 47 | 5311 |
| 45 and 107 | 4815 |
| 134 and 114 | 7638 |
| 196 and 200 | 9800 |