Least Common Multiple (LCM) of 16 and 170
The least common multiple (LCM) of 16 and 170 is 1360.
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 16 and 170?
First, calculate the GCD of 16 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 170 = 0 remainder 16 |
| 2 | 170 ÷ 16 = 10 remainder 10 |
| 3 | 16 ÷ 10 = 1 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 107 | 11770 |
| 155 and 137 | 21235 |
| 134 and 195 | 26130 |
| 193 and 57 | 11001 |
| 115 and 126 | 14490 |