Least Common Multiple (LCM) of 20 and 170
The least common multiple (LCM) of 20 and 170 is 340.
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 170?
First, calculate the GCD of 20 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 170 = 0 remainder 20 |
| 2 | 170 ÷ 20 = 8 remainder 10 |
| 3 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 114 | 7752 |
| 147 and 82 | 12054 |
| 200 and 146 | 14600 |
| 141 and 24 | 1128 |
| 108 and 30 | 540 |