Least Common Multiple (LCM) of 105 and 175
The least common multiple (LCM) of 105 and 175 is 525.
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 105 and 175?
First, calculate the GCD of 105 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 175 = 0 remainder 105 |
| 2 | 175 ÷ 105 = 1 remainder 70 |
| 3 | 105 ÷ 70 = 1 remainder 35 |
| 4 | 70 ÷ 35 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 175 | 700 |
| 98 and 38 | 1862 |
| 101 and 11 | 1111 |
| 15 and 154 | 2310 |
| 56 and 26 | 728 |