Least Common Multiple (LCM) of 118 and 170
The least common multiple (LCM) of 118 and 170 is 10030.
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 118 and 170?
First, calculate the GCD of 118 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 170 = 0 remainder 118 |
| 2 | 170 ÷ 118 = 1 remainder 52 |
| 3 | 118 ÷ 52 = 2 remainder 14 |
| 4 | 52 ÷ 14 = 3 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 186 | 27714 |
| 139 and 64 | 8896 |
| 46 and 18 | 414 |
| 180 and 20 | 180 |
| 148 and 156 | 5772 |