Least Common Multiple (LCM) of 175 and 47
The least common multiple (LCM) of 175 and 47 is 8225.
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 47?
First, calculate the GCD of 175 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 47 = 3 remainder 34 |
| 2 | 47 ÷ 34 = 1 remainder 13 |
| 3 | 34 ÷ 13 = 2 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 74 | 8510 |
| 59 and 164 | 9676 |
| 52 and 105 | 5460 |
| 40 and 178 | 3560 |
| 149 and 34 | 5066 |