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 |
|---|---|
| 89 and 154 | 13706 |
| 78 and 87 | 2262 |
| 130 and 120 | 1560 |
| 186 and 188 | 17484 |
| 154 and 158 | 12166 |