Least Common Multiple (LCM) of 20 and 174
The least common multiple (LCM) of 20 and 174 is 1740.
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 174?
First, calculate the GCD of 20 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 174 = 0 remainder 20 |
| 2 | 174 ÷ 20 = 8 remainder 14 |
| 3 | 20 ÷ 14 = 1 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 158 | 2844 |
| 28 and 49 | 196 |
| 51 and 34 | 102 |
| 193 and 155 | 29915 |
| 116 and 191 | 22156 |