Least Common Multiple (LCM) of 119 and 176
The least common multiple (LCM) of 119 and 176 is 20944.
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 119 and 176?
First, calculate the GCD of 119 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 176 = 0 remainder 119 |
| 2 | 176 ÷ 119 = 1 remainder 57 |
| 3 | 119 ÷ 57 = 2 remainder 5 |
| 4 | 57 ÷ 5 = 11 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 14 | 630 |
| 123 and 166 | 20418 |
| 149 and 198 | 29502 |
| 67 and 93 | 6231 |
| 24 and 32 | 96 |