Least Common Multiple (LCM) of 170 and 63
The least common multiple (LCM) of 170 and 63 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 170 and 63?
First, calculate the GCD of 170 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 63 = 2 remainder 44 |
| 2 | 63 ÷ 44 = 1 remainder 19 |
| 3 | 44 ÷ 19 = 2 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 187 | 1870 |
| 167 and 164 | 27388 |
| 134 and 124 | 8308 |
| 173 and 73 | 12629 |
| 121 and 47 | 5687 |