Least Common Multiple (LCM) of 20 and 175
The least common multiple (LCM) of 20 and 175 is 700.
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 20 and 175?
First, calculate the GCD of 20 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 175 = 0 remainder 20 |
| 2 | 175 ÷ 20 = 8 remainder 15 |
| 3 | 20 ÷ 15 = 1 remainder 5 |
| 4 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 116 | 5220 |
| 185 and 10 | 370 |
| 10 and 150 | 150 |
| 137 and 43 | 5891 |
| 23 and 194 | 4462 |