Least Common Multiple (LCM) of 170 and 104
The least common multiple (LCM) of 170 and 104 is 8840.
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 104?
First, calculate the GCD of 170 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 104 = 1 remainder 66 |
| 2 | 104 ÷ 66 = 1 remainder 38 |
| 3 | 66 ÷ 38 = 1 remainder 28 |
| 4 | 38 ÷ 28 = 1 remainder 10 |
| 5 | 28 ÷ 10 = 2 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 32 | 544 |
| 33 and 65 | 2145 |
| 29 and 108 | 3132 |
| 161 and 121 | 19481 |
| 194 and 122 | 11834 |