Least Common Multiple (LCM) of 109 and 176
The least common multiple (LCM) of 109 and 176 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 109 and 176?
First, calculate the GCD of 109 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 176 = 0 remainder 109 |
| 2 | 176 ÷ 109 = 1 remainder 67 |
| 3 | 109 ÷ 67 = 1 remainder 42 |
| 4 | 67 ÷ 42 = 1 remainder 25 |
| 5 | 42 ÷ 25 = 1 remainder 17 |
| 6 | 25 ÷ 17 = 1 remainder 8 |
| 7 | 17 ÷ 8 = 2 remainder 1 |
| 8 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 154 | 8932 |
| 30 and 196 | 2940 |
| 195 and 88 | 17160 |
| 86 and 14 | 602 |
| 41 and 179 | 7339 |