Least Common Multiple (LCM) of 176 and 109
The least common multiple (LCM) of 176 and 109 is 19184.
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 176 and 109?
First, calculate the GCD of 176 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 109 = 1 remainder 67 |
| 2 | 109 ÷ 67 = 1 remainder 42 |
| 3 | 67 ÷ 42 = 1 remainder 25 |
| 4 | 42 ÷ 25 = 1 remainder 17 |
| 5 | 25 ÷ 17 = 1 remainder 8 |
| 6 | 17 ÷ 8 = 2 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 77 | 5775 |
| 175 and 26 | 4550 |
| 39 and 170 | 6630 |
| 165 and 48 | 2640 |
| 20 and 52 | 260 |