Least Common Multiple (LCM) of 176 and 123
The least common multiple (LCM) of 176 and 123 is 21648.
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 123?
First, calculate the GCD of 176 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 123 = 1 remainder 53 |
| 2 | 123 ÷ 53 = 2 remainder 17 |
| 3 | 53 ÷ 17 = 3 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 105 | 2835 |
| 196 and 117 | 22932 |
| 44 and 54 | 1188 |
| 154 and 67 | 10318 |
| 67 and 45 | 3015 |