Least Common Multiple (LCM) of 114 and 170
The least common multiple (LCM) of 114 and 170 is 9690.
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 114 and 170?
First, calculate the GCD of 114 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 170 = 0 remainder 114 |
| 2 | 170 ÷ 114 = 1 remainder 56 |
| 3 | 114 ÷ 56 = 2 remainder 2 |
| 4 | 56 ÷ 2 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 14 | 910 |
| 100 and 77 | 7700 |
| 156 and 95 | 14820 |
| 84 and 47 | 3948 |
| 87 and 166 | 14442 |