Least Common Multiple (LCM) of 122 and 176
The least common multiple (LCM) of 122 and 176 is 10736.
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 122 and 176?
First, calculate the GCD of 122 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 176 = 0 remainder 122 |
| 2 | 176 ÷ 122 = 1 remainder 54 |
| 3 | 122 ÷ 54 = 2 remainder 14 |
| 4 | 54 ÷ 14 = 3 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 18 | 1854 |
| 163 and 169 | 27547 |
| 144 and 38 | 2736 |
| 153 and 89 | 13617 |
| 115 and 183 | 21045 |