Least Common Multiple (LCM) of 63 and 170
The least common multiple (LCM) of 63 and 170 is 10710.
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 63 and 170?
First, calculate the GCD of 63 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 170 = 0 remainder 63 |
| 2 | 170 ÷ 63 = 2 remainder 44 |
| 3 | 63 ÷ 44 = 1 remainder 19 |
| 4 | 44 ÷ 19 = 2 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 34 | 5746 |
| 60 and 68 | 1020 |
| 98 and 140 | 980 |
| 60 and 175 | 2100 |
| 18 and 126 | 126 |