Least Common Multiple (LCM) of 110 and 175
The least common multiple (LCM) of 110 and 175 is 3850.
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 110 and 175?
First, calculate the GCD of 110 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 175 = 0 remainder 110 |
| 2 | 175 ÷ 110 = 1 remainder 65 |
| 3 | 110 ÷ 65 = 1 remainder 45 |
| 4 | 65 ÷ 45 = 1 remainder 20 |
| 5 | 45 ÷ 20 = 2 remainder 5 |
| 6 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 72 | 720 |
| 152 and 115 | 17480 |
| 144 and 114 | 2736 |
| 114 and 73 | 8322 |
| 172 and 116 | 4988 |