Least Common Multiple (LCM) of 61 and 175
The least common multiple (LCM) of 61 and 175 is 10675.
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 61 and 175?
First, calculate the GCD of 61 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 175 = 0 remainder 61 |
| 2 | 175 ÷ 61 = 2 remainder 53 |
| 3 | 61 ÷ 53 = 1 remainder 8 |
| 4 | 53 ÷ 8 = 6 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 |
|---|---|
| 104 and 172 | 4472 |
| 55 and 84 | 4620 |
| 170 and 133 | 22610 |
| 104 and 49 | 5096 |
| 165 and 30 | 330 |