Least Common Multiple (LCM) of 176 and 199
The least common multiple (LCM) of 176 and 199 is 35024.
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 199?
First, calculate the GCD of 176 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 199 = 0 remainder 176 |
| 2 | 199 ÷ 176 = 1 remainder 23 |
| 3 | 176 ÷ 23 = 7 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 27 | 1728 |
| 106 and 184 | 9752 |
| 68 and 139 | 9452 |
| 135 and 21 | 945 |
| 111 and 134 | 14874 |