Least Common Multiple (LCM) of 117 and 170
The least common multiple (LCM) of 117 and 170 is 19890.
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 117 and 170?
First, calculate the GCD of 117 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 170 = 0 remainder 117 |
| 2 | 170 ÷ 117 = 1 remainder 53 |
| 3 | 117 ÷ 53 = 2 remainder 11 |
| 4 | 53 ÷ 11 = 4 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 37 | 5180 |
| 88 and 146 | 6424 |
| 115 and 114 | 13110 |
| 66 and 194 | 6402 |
| 128 and 74 | 4736 |