Least Common Multiple (LCM) of 175 and 49
The least common multiple (LCM) of 175 and 49 is 1225.
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 175 and 49?
First, calculate the GCD of 175 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 49 = 3 remainder 28 |
| 2 | 49 ÷ 28 = 1 remainder 21 |
| 3 | 28 ÷ 21 = 1 remainder 7 |
| 4 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 71 | 2414 |
| 170 and 90 | 1530 |
| 161 and 105 | 2415 |
| 22 and 42 | 462 |
| 187 and 90 | 16830 |